Question

If alpha and beta are zeroes of the polynomial f(x)=x^2-x-k such that alpha minus beta is equal to 9 find k

Answer 1

$from \: the \: polynomial \\ \alpha + \beta = 1 - - - (1) \\ given \\ \alpha - \beta = 9 - - - (2) \\ (1) + (2) \: gives \\ 2 \alpha = 10 \\ \alpha = 5 \\ from \: (1) \\ \beta = 1 - 5 = - 4$
$from \: the \: polynomial \\ \alpha \beta = - k \\ k = - \alpha \times \beta = - 5 \times - 4 = 20$

Answer 2

Answer:

The value of k is 20

Step-by-step explanation:

Given alpha and beta are zeroes of the polynomial

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

we have to find the value of k if α-β=9

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

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

The value of k is 20