If sum of squares of zeros of the quadratic polynomial $f (x) = x^{2} - 8 x + k$ is 40, find the value of k.

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Solution

Let a,b be the zeros of the polynomial.Then,
$a + b = 8$ and $a b = k$
Given,
$a^{2} + b^{2} = 40$
$(a + b)^{2} - 2 a b = 40$
$64 - 2 k = 40$
$2 k = 24$
$k = 12$

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