Question

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Alpha, Beta are zeroes of the quadratic polynomial x^2-(k+6)x +2 (2k-1). Find the value of k if alpha+beta = 1/2 alphabeta.
(Ans: 7)

Class 10th

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Answer 1

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 .

Answer 2

thats it.............