Question

If the sum of the squares of zeros of the polynomial f(x) = x² – 8x + k is 40, find the value of k.

Answer 1

Given: Let the zeros be α and β of f(x) = x² – 8x + k. 

Then α + β = 8 and αβ = k.

α² + β² = (α + β)² – 2αβ

= 8² – 2k

= 64 – 2k

Set 64 – 2k = 40   ...(Given)

So, 2k = 24 and k = 12.