Determine the nature of the roots of \(4x^2 - 12x + 9 = 0\) and hence find the roots.

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

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Answer: Roots are real and equal; \(x = \dfrac{3}{2}\)

\(a = 4\), \(b = -12\), \(c = 9\)

\(\Delta = (-12)^2 - 4(4)(9) = 144 - 144 = 0\), so the roots are real and equal.

Each root \(= -\dfrac{b}{2a} = \dfrac{12}{8} = \dfrac{3}{2}\). (Indeed \(4x^2 - 12x + 9 = (2x - 3)^2\).)

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

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