If - - - are zeros of x 2- k -6 x -2 x -1- Find k if -

Given α and β are zeroes of the polynomial f(x) = ax2 + bx + c α+ β = b / a αβ = c / a. If α and β are zeroes of the quadratic polynomial p(x)=x2 (k 6)x+(2k ...

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Mathematics

Formation of a Quadratic Equation From It's Roots

If α , β are ...

Question

If α,β are zeros of x²-(k-6)x+(2x+1) . Find k if α+β=αβ

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Solution

Given α and β are zeroes of the polynomial f(x) = ax² + bx + c

α+ β = -b / a αβ = c / a.
If α and β are zeroes of the quadratic polynomial p(x)=x²-(k-6)x+(2k+1) and α+β= αβ α+ β = k - 6 and αβ = 2k + 1

Given that α + β = αβ

k - 6 = 2k + 1

∴ k = - 7 .

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If α,β are zeros of x²-(k-6)x+(2x+1) . Find k if α+β=αβ

Given α and β are zeroes of the polynomial f(x) = ax2 + bx + c α+ β = -b / a αβ = c / a. If α and β are zeroes of the quadratic polynomial p(x)=x2-(k-6)x+(2k+1) and α+β= αβ α+ β = k - 6 and αβ = 2k + 1 Given that α + β = αβ k - 6 = 2k + 1 ∴ k = - 7 .

Given α and β are zeroes of the polynomial f(x) = ax² + bx + c

α+ β = -b / a αβ = c / a.
If α and β are zeroes of the quadratic polynomial p(x)=x²-(k-6)x+(2k+1) and α+β= αβ α+ β = k - 6 and αβ = 2k + 1

Given that α + β = αβ

k - 6 = 2k + 1

∴ k = - 7 .