Question

if alpha and beta are the zeroes of the quadratic polynomial 6x^2-(k+1)-7x such that one zero is11/6 more than the other,find the value of k
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Answer 1

Given,

x^2 −6x+k

Where,

α+β= a)−b =−1/−6 =6

α/β= a/c = 1/k =k

We have,

3α+2β=20

=>α+2α+2β=20

=>α+2(α+β)=20

=>α+2(6)=20

=>α=20−12

=>α=8

Putting the value in equation as α is the zero of the polynomial,we get,

x^2−6x+k

=(8)^2 −6(8)+k

=64−48+k

=16+k

=>k=−16