Question

If alpha and beta are zeroes of polynomial f(x)=x2-x-k such that alpha -beta =9 , find k

Answer 1

here's your answer
hope it helps

Answer 2

Hey there!

given α , β are zeroes of the polynomial f ( x).

Also, f ( x ) = x² - x - k.

We know that for a Quadratic polynomial, Sum of roots = - ( Coefficient of x) : Coefficient of x²

So,

α + β = - ( - 1) / 1 = 1

Also,

$\mathbf{\alpha-\beta=9}$ , from the question.

Solving the both equations, You would get

$\boxed {α = 5 , β = - 4.}$

Now,

We know that,

Product of roots = 5 × - 4 = - 20

But, According to the given equation, Product of roots = - k.

Equating both of them,

-k = - 20

$\boxed{\boxed{k = 20}} \: \:$

Therefore, The value of k is 20.