If the sum of the squares of the roots of the equation x^{2}-14x+k=0 is 100, then what is the value of k?

Explanation

Let roots be \alpha and \beta. Sum of roots \alpha+\beta=14 and product \alpha\beta=k. We are given \alpha^2+\beta^2=100. Using (\alpha+\beta)^2 - 2\alpha\beta = \alpha^2+\beta^2 \implies 14^2 - 2k = 100 \implies 196 - 100 = 2k \implies k = 48.

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