Question

Find p(-3) in the given polynomial p(x)=x2+5x-24

Answer 1

Answer:

see the picture okay....

Answer 2

Answer:

This is your Answer hope it helps you

Step-by-step explanation:

If α and β are the zeros of the equation,

It means that :

x = α or x = β

Since α - β = 1, therefore

α = β + 1

x= β + 1 or x = β

The factors of x2 - 5x + k are (x - β) and (x - β - 1)

(x - β)*(x - β - 1) = x2 - 5x + k

x2 - βx - x - βx + β2 + β = x2 - 5x + k

x2 - 2βx - x + β2 + β = x2 - 5x + k

Subtract x2 from both sides,

- 2βx - x + β2 + β = - 5x + k

Equating the like terms on both sides, we see that

- 2βx - x = - 5x (equation 1)and

β2 + β = k (equation 2)

From equation 1,

- 2βx - x = - 5x

- x(2β + 1) = - 5x

Divide both sides by -x

2β + 1 = 5

2β = 4, therefore β = 2

Putting β as 2 in equation 2, we have

2^2 + 2 = k

k = 6

To confirm, we first find α,

α = β + 1

α = 2 + 1 = 3

(x -α) (x - β) = x2 - 5x + k

(x -3) (x - 2) = x2 - 5x + k

x2 - 2x - 3x + 6 = x2 - 5x + k

x2 - 5x + 6 = x2 - 5x + k

Therefore, k = 6