Question

If a and B are zeroes of the polynomial f (x) =
x2-x-k, such that a- B = 9, find k.
​

Answer 1

Answer:

k=2

Explanation:

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,

, from the question.

Solving the both equations, You would get

α=5 and 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

k=20

Therefore, The value of k is 20.