Question

If α and β are zeroes of the quadratic polynomial p(x) = x^2 -(k+6)x+2(2k-1). Then find the value of k, if α+β=αβ/2

Answer 1

solution

sum of zeroes= -b/a

@+ß= -{-(k+6)}/1= k+6

@*ß= c/a= 4k -2

Now,@+ß= @ß/2

=> k+ 6= 4k - 2/2

=> k + 6= 2k - 1

=> -K = -7

=> k = 7

NOTE__@= alpha & ß= beta

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hope it helps☺☺

Answer 2

if α, β are roots

then αβ = c/a
α+β = -b/a

α+β = αβ/2

-b/a = c/a/2

-b/a = c/2a

-b = c/2

- [-(k+6)] = 2(2k-1)/2

k+6 = 2k-1

k = 7