If \(\alpha\) and \(\beta\) are the roots of \(x^2 - 5x + 3 = 0\), form the quadratic equation whose roots are \(\alpha^2\) and \(\beta^2\).

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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Answer: \(x^2 - 19x + 9 = 0\)

\(\alpha + \beta = 5\), \(\alpha\beta = 3\).

Sum of new roots: \(\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = 25 - 6 = 19\)

Product of new roots: \(\alpha^2\beta^2 = (\alpha\beta)^2 = 9\)

Required equation: \(x^2 - 19x + 9 = 0\)

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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