# If sum of the square of zeros of the quadratic polynomial f(x) =x^2-8x+k is 40, find the value of k

Solution: Let $\\\alpha ,\beta$ be the zeros of the polynomial $\\ f(x)=x^2-8x+k$ Then,

$\\(\alpha +\beta )=8$ And $\\\alpha \beta =k$

It is given that

$\\\alpha ^2+\beta ^2=40\\ \\\Rightarrow (\alpha +\beta )^2-2\alpha \beta =40\\ \\\Rightarrow 64-2k=40\\ \\\Rightarrow 2k=24\\ \\\Rightarrow k=12$

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