If K is the ratio of the roots of the polynomial x²+px-q, the value of k/1+k² is:​

Answers

Answer 1

[tex]\large\underline{\sf{Solution-}}[/tex]

Given Polynomial:

[tex] \rm \longmapsto f(x) = {x}^{2} + px - q[/tex]

Let α and β be the zeros of f(x)

Then:

[tex] \rm \longmapsto \alpha + \beta = - p[/tex]

[tex] \rm \longmapsto \alpha \beta = - q[/tex]

Now, it's given that:

[tex] \rm \longmapsto k = \dfrac{ \alpha }{ \beta } [/tex]

Consider the expression given:

[tex] \rm = \dfrac{k}{1 + {k}^{2} } [/tex]

[tex] \rm = \dfrac{ \dfrac{ \alpha }{ \beta } }{1 + { \dfrac{ \alpha {}^{2} }{ \beta {}^{2} } }} [/tex]

[tex] \rm = \dfrac{ \dfrac{ \alpha }{ \beta } }{ { \dfrac{ \alpha {}^{2} + { \beta }^{2} }{ \beta {}^{2} } }} [/tex]

[tex] \rm = \dfrac{ \alpha }{ { \dfrac{ \alpha {}^{2} + { \beta }^{2} }{ \beta } }} [/tex]

[tex] \rm = \dfrac{ \alpha \beta }{\alpha {}^{2} + { \beta }^{2} } [/tex]

[tex] \rm = \dfrac{ \alpha \beta }{ {( \alpha + \beta )}^{2} - 2 \alpha \beta } [/tex]

[tex] \rm = \dfrac{ - q }{ {p}^{2} + 2q} [/tex]


Related Questions

75.25-11.92
what is the answer

Answers

Answer:

63.33

Pretty easy if you use a calculator

Graph y ≤ 1 - 3x.
(picture added)

Answers

When I graphed this equation myself I got answer in the top right. (My graph can be seen below)

(7,0). (3.6)
What is the slope?

Answers

Step-by-step explanation:

given,

points = (7,0) & (3,6)

we know,

slope = y_2 - y_1 / x_2 - x_1

now,

6 - 0/3-7

6/-4

-1.5 or 3/-2

therefore , slope of line is -1.5 OR In the form of fraction it is 3/-2.

hope this answer helps you dear...take care and may u have a great day ahead!

PLEASE HURRY Which of the following is NOT a solution in the solution region.




(-4, -1)
(-4, -1)

(0, -4)
(0, -4)

(5, 2)
(5, 2)

(2, -8)

Answers

Answer:

Need full problem.

Step-by-step explanation:

Need full problem.

Solve for X in a given interval. csc x= 2, for 0 < x < pi/2

Answers

Answer:

x = π/6

Step-by-step explanation:

csc x=2

-> 1/sinx = 2

-> sin x = 1/2

x = π/6 or x =2π/3

for 0 less than or equal to x less than or equal to pi/ 2

-> x = π/6

Step-by-step explanation:

stan eric nam

When x = 3, evaluate: 4x

When x = -2, evaluate: x2 =

Answers

1) 12
2) -4
I hope this was correct?
4x = 4 × 3 = 12 x2 = -2 × 2 = -4 .

3x + 5y = 5 7x + 5y = 25 what would be x and y for them

Answers

I did substitute for this and at the end I got x=5 and y=-2

If Marisa’s hair grew 1 and 1/4 in. In 2 months, what was her hair growth in 1 month?

Answers

ANSWER:

1 AND 1/5

______________

HOPE IT HELPS YOU

CAN YOU BRAINLEST ME

Answer:

Step-by-step explanation:

hair grew 3/4 in. in 1 1/2 months? How long did her hair grow in one month? 1. See answer. Add answer+5 pts. The answer is 1/2.

series representation of



[tex]e[/tex]

Answers

[tex] \huge \underline \mathtt \colorbox{cyan}{ATTACHMENTS}[/tex]

All 3 are possible

Item 4
Which point has coordinates (−2, 1.5) ?




A

B

C

I don't know.


A coordinate grid with the x and y axis from negative 3 to 3, with each line on the graph representing a step of 1 fourth. Point A is 8 steps to the right and 6 steps up. Point B is 8 steps to the left and 6 points up. Point C is 6 steps to the left and 1 step up.

Answers

i’m pretty sure its B

Point B. is 8 steps to the left and 6 points up has coordinate points (-2,1.5).

What is a coordinate grid?

A coordinate grid is a plane in which we can graph 2D figures.

If we assume that each square box n the x-y plane is of 1 sq unit then the length of the sides of each box is 1 unit.

Now we can observe that 4 such sides or boxes have a value of 1 unit so we can say that the plane has been shrunk by a factor of 1/4.

If we observe point B which is 8 steps to the left and 6 points up we can conclude B( -8,6) and has a scale factor of (1/4).

∴ B(-2,1.5).

learn more about coordinate points here :

https://brainly.com/question/21950350

#SPJ2

What is the correct answer to this geometry question?

Answers

HI + IJ = HJ

=> x + 12 +  16 + x = 20

<=> 2x + 28 = 20

<=> 2x = -8

<=> x = -4

with x = -4 => HI = - 4 + 12 = 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

20 = 12 + 16 + 2x

20 - 12 - 16 = 2x

-8 = 2x

x = -4

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

check

20 = 12 + 16 + 2*-4

20 = 20

the answer is good

Which defines the relationship between the number -9 and its additive inverse?
A. -9x1= -9
B-9 +0= -9
C. (-9) X0 = 0
D. (-9) +9 = 0

Answers

The Additive Inverse Property states that the sum of a real number and its opposite is 0.

a + (-a) = 0.


Therefore, the correct answer is Option D): (-9) + 9 = 0


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How do you find the zero of a function by graphing?

Answers

Answer:

Look where the function intersects the x axis. The x coordinate of those points are the zeroes of the function

Step-by-step explanation:

Lauren is a waitress at a restaurant. Each day she works, Lauren will make a guaranteed wage of $30, however the additional amount that Lauren earns from tips depends on the number of tables she waits on that day. From past experience, Lauren noticed that she will get about $6 in tips for each table she waits on. How much would Lauren expect to earn in a day on which she waits on 17 tables? How much would Lauren expect to make in a day when waiting on t tables?

Answers

Answer:

132

Step-by-step explanation:

$6 x 17= 102

102+$30= $132

The perimeter of a rectangle is 28cm it’s length is more than 10cm more than it’s widith which equation can be used to find the dimensions

Answers

P = 2((10 + x) + x)

The perimeter of a rectangle is the sum of the length and width multiplied by 2

P = 2(l + w)

[to simplify the expression]

P = 2 × (l + w)

[using x to represent the width]

w = x

l = x + 10

P = 2 × ((10 + x) + x)

P = 2((10 + x) + x)

Any experts, help please.

Answers

1: x to the 2nd power x= the number
2 divide by 3

Item 1
Which symbol correctly compares these fractions?

−3/5□−2/3


>

<

=

Answers

Answer:

The answer is -3/5 > -2/3

Step-by-step explanation:

okay

Answer:

the answer is. ......

−3/5>2/3

(solve equation)

7b=84

Answers

Answer:

b = 12

Step-by-step explanation:

7b = 84

We can break down 7b as 7 x b

7 x b = 84

We divide both sides by 7:

7 x b ÷ 7 = 84 ÷ 7

b = 12

-Chetan K

Which equation reveals the minimum or the maximum value of f(x) without changing the form of the equation?

A f(x) = (x – 1)2 + 2

6 f(x) = x2 – 2 – x + 1

© f(x) = x2 – 2x + 1

D f(x)= (x - 1)(x - 1)

Answers

Answer:

A): f(x) = (x – 1)² + 2

Step-by-step explanation:

The quadratic function, f(x) = (x – 1)² + 2 is in vertex form: y = a(x - h)² + k, where:

The vertex of the graph is (h,k).The value of a determines whether the graph opens up or down. If a is positive, the graph opens up and the vertex is its minimum point. If a is negative, then the graph opens down, and the vertex is its maximum point. The value of h determines how far left or right the parent function is translated. The value of k determines how far up or down the parent function is translated.

The function, f(x) = (x – 1)² + 2, provides the pertinent information that allows us to determine the parabola's minimum value, as the value of a is a positive, which implies that the parabola is upward facing, and the vertex, (1, 2) is the minimum point.

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Solve for h in terms of g and u


4u²(2u²) /g = -2u²h -gh²/2 +h

Answers

9514 1404 393

Answer:

  h = (1 -2u² ± √(1 -4u²-12u⁴))/g

Step-by-step explanation:

This is a quadratic in h, so there are two solutions.

Written in standard form, the given equation is ...

  (-g/2)h² +(1-2u²)h -8u⁴/g = 0

The quadratic formula tells you the solution for h is ...

  h = (-(1 -2u²) ±√((1 -2u²) -4(-g/2)(-8u⁴/g)))/(2(-g/2))

  h = (2u² -1 ± √(4u⁴ -4u² +1 -16u⁴))/-g . . . . . simplify

  h = (1 -2u² ± √(1 -4u²-12u⁴))/g . . . . . . . . collect terms

On his bookshelf, Adam has the difference between two-thirds of Brett's books and two-thirds of Charlie's books. If Brett has 84 books and Charlie has 27 books, how many books does Adam have?

Answers

Answer:

30 books

Step-by-step explanation:

Decrease £180 by 25%

Answers

Answer:

the answer is 135 pounds

Answer:

180 - 25% = 135

Hope this helps

Please help! I will mark brainliest!

Answers

Answer:

1. is 283.9953

Step-by-step explanation:

360 degrees - 76.0047 degrees is 283.9953

True or false??????????

Answers

Answer:

True

Step-by-step explanation:

Answer:

TRue

Step-by-step explanation:

Did that also

no spams
need a well explained ans
if u don't know stay out of the question​

Answers

The three inside angles need to equal 170 when added together.

When two sides are the same which is shown by the little lines through the sides the two bottom angles are the same.

1. X = 170-80-80 = 20

2. X = 180-75-75 = 30

3. X = 180-70 = 110/2 = 55

Step-by-step explanation:

1) x+80°+80°=180°

x=180°-160°

x=20°.

2) as it is a isosceles triangle, y =75°.

x+75°+75°=180°

x=180°-150°

x=30°.

3) 2x+70°=180°

2x=110°

x=55°.

hope all these helps you.

I need help on Absolute Value Equations!
|6x−18|=−1

Answers

Answer:

there is no solution

Step-by-step explanation:

no absolute value can be negative

Answer:

no solutions

Step-by-step explanation:

1. There's no solution to this equation because absolute values cannot be less than 0.

solve the question in the picture

Answers

Answer:

the answer you need is in the pic above

Answer above is correcttttttt

What is an equation of the line that passes through the point (−1,−3) and is parallel to the line 6x-y=1?

Answers

Answer:

y = 6x + 3

Step-by-step explanation:

6x - y = 1

6x -1 = y

Slope = 6

Point (-1,-3)

y-intercept = -3 - (6)(-1)

= -3 + 6 = 3

y = 6x + 3

Please answer bOtH questions ❤ tysm
Pablo has ten dollars. He wants to buy 7 packs of gum. Rach pack of gum costs $1.50. Does he have enough? How do you know? ​

Answers

Answer:

no. it costs $10.5

Step-by-step explanation: first you multiply 1.5 ( how much it costs) by 7 ( how much hes gonna get) and that equals 10.5. as you can see, thats 5 cents more than 10 dollars

Answer:

No, he does not have enough. Here's why.

Step-by-step explanation:

Pablo has 10 dollars, and each pack of gum costs $1.50. He wants 7 packs, so we do $1.50 times 7(for 7 packs.)

$1.50 times 7 is $10.50, which leaves Pablo 50 cents short.

He does not have enough money.

I hope this helps you! Have a great day.

A student earned a grade of 80% on a math test that had 20 problems.How many problems on this test did the student answer correctly

Answers

Answer:

16 problems

Step-by-step explanation:

1. First, we must know that to find how many problems the student solved, we have to multiply the percentage he got by the total number of problems.

2. (Solving)

[tex]\frac{80}{100}*20[/tex] [tex]\frac{4}{5} *20[/tex] [tex]\frac{80}{5}[/tex] [tex]16[/tex]

Therefore, the student answered 16 problems correctly.

Answer:

16

Step-by-step explanation:

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