Question

If alpha and beta are the zeros of polynomial P of x 7 x square - 8 x + K such that Alpha minus beta is equal to 2 then find the value of k

Answer 1

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Answer 2

Answer:

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