Numerical answer
The sum of the roots of a quadratic equation is 10 and the product of the roots is 21. Find the sum of the squares of the roots.
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Answer: 58
For roots p and q: p+q = 10, pq = 21. Sum of squares p²+q² = (p+q)² − 2pq = 10² − 2×21 = 100 − 42 = 58. (The roots themselves are 3 and 7, since x²−10x+21=0 factors as (x−3)(x−7); check: 3²+7² = 9+49 = 58.)
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