Question

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

Answer 1

Step-by-step explanation:

Given that α and β are the roots of the polynomial f(x)=x

2

−x−k

such that α−β=9

To find k,

Squaring on both sides of the equation α−β=9,gives,

α

2

+β

2

−2αβ=81

⟹(α+β)

2

−4αβ=81

⟹1+4k=81

⟹4k=80

⟹k=20

The sum and product of the roots are determined from the given polynomial.