Does every quadratic equation have at
least one real solution? Explain. (1 point)
A. Yes. When the discriminant is zero, there is exactly one solution. When the discriminant is not zero, there are two unique solutions.
B. No. When the discriminant is greater than zero, there are no real solutions.
C. Yes. When the discriminant is zero, there are two unique solutions. When the discriminant is not zero, there is exactly one solution.
D. No. When the discriminant is less than zero, there are no real solutions.

Answers

Answer 1

Answer:

D. No. When the discriminant is less than zero, there are no real solutions.

Step-by-step explanation:

We have to notice that quadratic equations are second order polynomials whose standard form is:

[tex]y = a\cdot x^{2}+b\cdot x + c \cdot x[/tex], [tex]\forall \,a,b,c\,\in\,\mathbb{R}[/tex]

The factorized form of this polynomial is:

[tex]y = (x-r_{1})\cdot (x-r_{2})[/tex]

Where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the roots of the quadratic equation, which may be real or complex.

If we equalize [tex]y[/tex] to zero and make algebraic handling, we can get the value of each root anatically by the Quadratic Formula:

[tex]r_{1,2} = \frac{-b\pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]

Where [tex]b^{2}-4\cdot a\cdot c[/tex] is known as the discriminant. Then, we should remember the following rules:

i) If discriminant is greater than zero, then the quadratic equation has two different real roots.

ii) If discriminant is zero, then the quadratic equation has two equal real roots.

iii) If discriminant is less than zero, then the quadratic function has two complex roots.

In consequence, we came to the conclusion that statement is false, as quadratic equation have all roots real or all complex, but not one real and the other complex.

In a nutshell, the correct answer is D.


Related Questions

How can you approximate the value of VI 30 ?

Answers

Answer:

VI is 6

Step-by-step explanation:

Answer:

VI is 6

Step-by-step explanation:

At Becky's Restaurant, 10 out of 25 customers order wheat rolls. The rest of the customers order cornbread. Which does NOT represent the part of the customers who order wheat rolls

Answers

Answer:

C. 25 ÷ 10

Step-by-step explanation:

A. 10/25

B. 2/5

C. 25 ÷ 10

D. 0.4

Total customers at Becky's restaurant = 25

Customers who order wheat rolls = 10

It means 10 out of 25 customers order wheat rolls

That is

10 / 25

Dividing both numerator and denominator by 5

= 2 / 5

2/5 in decimal

= 0.4

The option Which does NOT represent the part of the customers who order wheat rolls

is 25/10

Option C. 25 ÷ 10

The figure shown has two parallel lines cut by a transversal: A pair of parallel lines is shown, crossed by a transversal. Angles are identified as 1, 2, 3, 4, 5, 6, 7, and 8. Angles 1-4 are on the top line clockwise from upper left. Angles 5-8 are on the lower line clockwise from upper left. Use the figure to complete the sentence. (4 points) ∠7 and ____ are alternate exterior angles. a ∠2 b ∠1 c ∠5 d ∠8

Answers

There are several relationships between angles within a transversal of parallel lines.

The complete statement is (b) ∠7 and ∠1 are alternate exterior angles

From the figure (see attachment), we have the following highlights

Angles 1 and 7 are both exterior anglesAngles 1 and 7 are both alternate angles

The above highlights mean that:

Angles 7 and 1 are alternate interior angles

Hence, the text that completes the blank is (b) ∠1

Read more about alternate interior angles at:

https://brainly.com/question/15685431

Answer:

b ∠1

Step-by-step explanation:

please solve for x, and give me an explanation on how you did so? 1/2x-1/3=5/6

Answers

Answer: x = 7/3

=======================================================

Explanation:

Fractions are a pain to deal with, so whenever possible I recommend you eliminate them. With equations like this, you can multiply both sides by the same number to do so. The question is: which number would that be?

If you pick on the LCD, then you'll be able to clear out the fractions. The LCD of 1/2, 1/3, and 5/6 is 6 since the LCM of the denominators is 6.

Multiply both sides by 6 to get

(1/2)x - 1/3 = 5/6

6*[ (1/2)x - 1/3 ] = 6(5/6)

6*(1/2)x - 6*(1/3) = 6(5/6)

3x - 2 = 5

------------

At this point, the fractions are gone. We can now solve like so

3x-2 = 5

3x-2+2 = 5+2 ... adding 2 to both sides

3x = 7

3x/3 = 7/3 .... dividing both sides by 3

x = 7/3

Answer:

x=5/6

Step-by-step explanation:

12x−13=5612x-13=56

Combine 1212 and xx.

x2−13=56x2-13=56

Move all terms not containing xx to the right side of the equation.

Add 1313 to both sides of the equation.

x2=56+13x2=56+13

To write 1313 as a fraction with a common denominator, multiply by 2222.

x2=56+13⋅22x2=56+13⋅22

Write each expression with a common denominator of 66, by multiplying each by an appropriate factor of 11.

Multiply 1313 and 2222.

x2=56+23⋅2x2=56+23⋅2

Multiply 33 by 22.

x2=56+26x2=56+26

Combine the numerators over the common denominator.

x2=5+26x2=5+26

Add 55 and 22.

x2=76x2=76

Multiply both sides of the equation by 22.

2⋅x2=2⋅

Add.
(2x2 - 2x) + (6x – 4)

Answers

2x^2 + 4x - 4

..........................

Answer:

x = {-2, -1}

Step-by-step explanation:

Combine like terms: 0 + -2 = -2

x = -2

Simplifying

x = -2

Combine like terms: 0 + -1 = -1

x = -1

Simplifying

x = -1

Antony borrowed 20,000,000 for 7 years his interest rate is 5% how much interest will he pay in all

Answers

Answer:

7,000,000

Step-by-step explanation:

[tex]Principal = 20,000,000\\Time =7\:years\\Rate = 5\%\\Simple\:interest =?\\\\Simple\:interest = \frac{Principal\times Rate\times Time}{100} \\\\S.I= \frac{20000000\times 5 \times 7}{100} \\\\S.I==\frac{700000000}{100}\\\\Simple\: interest=7000000[/tex]

The solution is, he will pay 7000000 interest in all.

What is interest?

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

Here, we have,

formula: I = Prt.

here, we have,

given that,

Antony borrowed 20,000,000 for 7 years his interest rate is 5%

i.e. we get,

P= 20,000,000

t = 7

r= 5%

and, we have to find I

so, we have,

I = P r t

 =20,000,000*5*7/100

 =7000000

Hence, he will pay 7000000 interest in all.

To learn more on interest click:

brainly.com/question/29335425

#SPJ3

write in standard form x2 + y = 2x -4​

Answers

Answer:

y = - x² + 2x - 4

Step-by-step explanation:

The equation of a parabola in standard form is

y = ax² + bx + c ( a ≠ 0 )

Given

x² + y = 2x - 4 ( subtract x² from both sides )

y = - x² + 2x - 4 ← in standard form


PLEASE HELP ME! I have de done this 10+ times

Determine intersections and unions of sets using interval notation

Given the sets A and B in interval notation,
A = (-∞, 2) U (2, + ∞) and
B= (-∞, - 1) U (-1, + ∞)

find A n B =

Answers

Answer:

Shown in the picture

4(-32x+5)-(-33x-26)=

Answers

Answer:

-95x+46

Step-by-step explanation:

4(-32x+5)-(-33x-26)=

-128x+20-(-33x-26)=

-128x+20+33x+26

-95x+46

Answer:

-95x-46

Step-by-step explanation:

4(-32x+5)-(-33x-26)=

-128x+20-(-33x-26)=

-128x+20+33x+26

-95x+46

A researcher randomly selected 30 people to participate in a study to investigate which of two materials, A or B, used in the heels of sneakers will last longer. The researcher is considering two design types for the study.

Design 1: Randomly assign 15 participants to wear sneakers with material A on their left feet and material B on their right feet. The remaining participants will wear sneakers with material B on their left feet and material A on their right feet.
Design 2: Randomly assign 15 participants to wear sneakers with material A on both feet and the remaining participants to wear sneakers with material B on both feet.
Which of the following best describes each design?

Answers

Answer:

Design 1

Step-by-step explanation:

Design one would work better because the students get to see both materials (each on one foot) and if they do the same things each day with both feet, they can test how the material works with the activity...If that makes sense

The question is an illustration of a random selection.

The descriptions of the designs are:

Design 1 is a matched pair designDesign 2 is a completely randomized design.

Design 1

From the question, we understand that:

15 participants wear material A on the left feet, and material B on the right feet.The other 15 wear material B on the left feet, and material A on the right feet.

The above description is a matched pair design, because half of the participants gets randomly assigned to material A and B, while the other half gets automatically assigned to the remaining materials.

Design 2

From the question, we understand that:

15 participants wear material A on both feetThe other 15 wear material B on both feet

The above description is a completely randomized design, because half of the participants gets randomly assigned to material A, while the other half gets randomly assigned to material B.

Read more about random selections at:

https://brainly.com/question/10678373

Point K is on line segment JL. Given JK = 5x + 7, JL = 2x+8, and KL = 4,

determine the numerical length of JL.

Answers

Answer:

The numerical length of JL is 6 units

Step-by-step explanation:

Here, we want to determine the numerical length of JL

Mathematically;

JL = JK + KL

2x + 8 = 5x + 7 + 4

2x + 8 = 5x + 11

5x -2x = 8-11

3x = -3

x = -1

But JL = 2x + 8

JL = 2(-1) + 8 = -2 + 8 = 6

Karen sells tickets at a movie theater. Last night she sold 128 tickets for a total of $1108. Adult's tickets cost $10 and children's tickets cost $6. How many of each kind of ticket did Karen sell?

Answers

Answer:

Adult's tickets 85

children's tickets 43

Step-by-step explanation:

x + y = 128

10x + 6y = 1108

x = 128 - y

10(128 - y) + 6y = 1108

1280 - 10y + 6y = 1108

1280 - 4y = 1108

-4y = 1108 - 1280

-4y = -172

y = -172/-4

y = 43

x = 128 - y

x = 128 - 43

x = 85

Simplify 7 -(-4) + 3(-6).
0-7
07
-9
9

Answers

it’s -7
7-(-4) is 7+4, which is 11
3 times -6 is -18
11 + -18 is -7
Answer: -7

7-(-4)=7+4=11
3(-6)= -18
11+(-18)= -7

Represent the following sentence as an algebraic expression, where "a number" is the letter x.
A number plus 2

Answers

Answer:

X+2

Step-by-step explanation:

A number is x plus 2

X+2

need help please help​

Answers

Answer:

  9 minutes

Step-by-step explanation:

The water volume in pool 1 starts at 50 gallons and increases at 2.3 gallons per minute. An expression for that volume could be ...

  v = 50 +2.3t

The water volume in pool 2 starts at 102.2 gallons and decreases at 3.5 gallons per minute. An expression for that volume could be ...

  v = 102.2 -3.5t

The volumes will be equal when ...

  50 +2.3t = 102.2 -3.5t

  5.8t = 52.2 . . . . . . . . . . . subtract 50-3.5t from both sides

  t = 52.2/5.8 = 9 . . . . . . . divide by the coefficient of t

After 9 minutes, the pools will contain the same amount of water.

_____

The equation 5.8t = 52.2 tells you the 52.2 gallon difference in volumes is being reduced at the rate of 5.8 gallons per minute. You don't really need the 'v' equations to figure that out.

i need an answer and explaination​

Answers

The answer for the question is 97
The answer is 96 because angel m

El cubo de la diferencia entre dos números cualquiera

Answers

Answer:

El cubo de la diferencia de dos cantidades es igual a la primera cantidad elevada al cubo menos tres veces la primera cantidad elevada al cuadrado por la segunda cantidad más tres veces la primera cantidad por la segundad cantidad al cuadrado menos la segunda cantidad al cubo.

Step-by-step explanation:

Answer:

lo siento, no puedo ayudarte

Step-by-step explanation:

Rewrite as a simplified fraction.
3.2 = ? 2 is repeating

Answers

Answer:

3

.

¯

2

=

29

9

Explanation:

Using the notation of a bar over a set of digits to denote their infinite repetition,

let  

x

=

3

.

¯

2

10

x

=

32

.

¯

2

10

x

x

=

32

.

¯

2

3

.

¯

2

=

29

9

x

=

29

x

=

29

9

This technique works in general. Set  

x

as your desired value, multiply by  

10

n

where  

n

is the number of digits repeating, and then subtract  

x

to eliminate the infinitely repeating portion. It then is just a matter of dividing by  

10

n

1

a

Step-by-step explanation:

x=536/165

you should know what to do since your in this part of the unit

I WILL MARK YOU BRAINLIEST. Xavier decorated his paper with stickers. He put 3 stickers on his paper. Each sticker is 1/8 inches wide and 2/5 inches long. What is the total area, in square inches, of all of the stickers Xavier used?

Answers

Answer:

3x1/8x2/5=3/20

Step-by-step explanation:

The length of a rectangle is 16m greater than the width. If the perimeter of a rectangle is 256m, what is the width of the rectangle?

Answers

Answer:

L=16+W

2W+2(16+W)=256

2W+32+2W=256

4W=224

W=56

jacob weights 36.4 pounds and alice. weights 42.275 pounds. how much do they weigh together

Answers

Answer:

78.675 pounds

Step-by-step explanation:

36.4 + 42.275 = 78.675 pounds

Answer:

it is 78.675 just round it to the nearest something which would be 78.68

Step-by-step explanation:

just add and round

A tree that grows 3 feet every 5 years is growing at a rate of ___ feet per year.'

Answers

[tex]\bf Step-by-step~explanation:[/tex]

Objective: You need to find the number of feet the tree grows every year (the unit rate).

[tex]\bf Steps:[/tex]

FIrst, we look at what we have now. The tree grows 3 feet every 5 years, so we have to divide 3 by 5 to get the number of feet the tree grows in one year.

[tex]\bf 3~feet~divided~by~5~years~=~Our~final~answer\\\frac{3}{5}=\frac{6}{10}~(multiplied~3~and~5~by~2)\\ \frac{6}{10} =0.6~feet[/tex]

[tex]\large\boxed {\bf Our~final~answer: ~0.6~feet~per~year}[/tex]

[tex]The~tree~grows~at~a~rate~of~0.6~feet~per~year.[/tex]

i need a little help with this equation 15-5+5^2

Answers

Answer:

35

Step-by-step explanation:

15-5+(5^2)

10+25

35

Need help i don't understand

Answers

The second one brother

What is the slope of a line that passes through 41-50

Answers

Answer:

-15/7

Step-by-step explanation:

The formula for slope is y2-y1/x2-x1 so replace the variables with -8-7/3-(-4) and solve which gets you -15/7

Translate sentence into an equation. Then ſind each number.
1. Seven more than three times a number is 16.
How to translate it

Answers

Answer:

This is the equation

Step-by-step explanation:

7 + 3x = 16

Please mark as brainliest.

Please help! (Will give brainliest answer and hearts) Thank you and have a nice day!

Answers

Point W since the X is 2 and the Y is 5.5

Answer:

W

Step-by-step explanation:

so you go to the right 2 times then you go down 5 and a half times (where the negative numbers are) and then you get the answer here is a picture so you can understand a little better, I hope this helps you :)

The area of a rectangular wall of a barn is 252 square feet. Its length is 10 feet longer than twice its width. Find the length and width of the wall of the barn.

Answers

Answer: Length = 28 feet and width = 9 feet

Step-by-step explanation:

Let x = width of the wall.

Then, Length of the wall =  10+2x

Since , Area of rectangle = length x width

Then, as per given,

[tex]252= (10+2x)x\\\\\Rightarrow\ 252=10x+2x^2\\\\\Rightarrow\ 2x^2+10x-252=0\\\\\Rightarrow\ x^2+5x-126=0\\\\\Rightarrow\ x^2+14x-9x-126=0\\\\\Rightarrow\ (x+14)-9(x+14)=0\\\\\Rightarrow\ (x+14)(x-9)=0\\\\\Rightarrow\ x=-14 \ or \ x= 9[/tex]

Since width cannot be negative , so x = 9

So width = 9 feet and length = 10+2(9)=10+18 = 28 feet

Hence, length is 28 feet and width is 9 feet of the wall of the barn.

Find the LCM of 30, 45, 60 and 90.​

Answers

Answer:180

Step-by-step explanation:

Simplify the expression: 1–7v+7v+9–2

Answers

Answer: 8

Step-by-step explanation:

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