If α and β are the zeroes of a quadratic Polynomial such that α + β = 24 , α - β = 8 . Find a quadratic Polynomial having α and β as it's zeroes.

α + β = 24 -- equation (1)

α - β = 8 -- equation (2).

A quadratic Polynomial having α and β as it's zeroes.

We know that,

(a + b)² - (a - b)² = 4ab

⟹ (α + β)² - (α - β)² = 4ab

Substitute the values from equations (1) & (2).

⟹ (24)² - (8)² = 4αβ

⟹ 576 - 64 = 4αβ

⟹ 512/4 = αβ

⟹ αβ = 128

Now,

General form of a Quadratic equation is x² - (sum of the zeroes)x + Product of the zeroes = 0.

We have:

Sum of the zeroes = 24

Product of the zeroes = 128.

So,

⟹ Required quadratic Polynomial = x² - 24x + 128

(a + b)² - (a - b)² = 4ab

Proof:

⟹ (a + b)(a + b) - (a - b)(a - b) = 4ab

⟹ a(a + b) + b(a + b) - [ a(a - b) - b(a - b) ] = 4ab

⟹ a² + ab + ab + b² - (a² - ab - ab + b²) = 4ab

⟹ a² + 2ab + b² - a² + ab + ab - b² = 4ab

⟹ 4ab = 4ab

I hope it will help you.

Regards.

ANSWER

α+β=24

α−β=8

(α−β)

2

=(α+β)

2

−4αβ=8

2

or,24

2

−4αβ=64

or,4αβ=576−64=512

or,αβ=128

⇒x

2

−(α+β)x+αβ=0

or,x

2

−24x+128=0

Hence x

2

−24x+128=0 is the quadratic polynomial for the required condition

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

the answer is 0.000652422

but if you ment to ask what is 6131 divided by 4, it is 1532.75.

step-by-step explanation: