Question

If alpha and beta are zeroes of the polynomial f(x)=x^2-x-k, such that alpha minus beta is 9. Find k

Answer 1

Answer of your problem is that
alpha = 5
Beta = -4
k = alpha * beta = 20

Answer 2

Answer:

k=20

Step-by-step explanation:

The given polynomial is:

$f(x)=x^{2}-x-k$

If α and β are the zeroes of the given polynomial, then the sum of zeroes that is:

α+β=1 and the product of the zeroes that is αβ=-k

Also, it is given that α-β=9, then using α+β=1 and α-β=9 and solving by the elimination method, we get α=5 and β=-4.

Now, αβ=-k⇒5(-4)=-k

⇒k=20