Question:medium

Let \((n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0\) be a quadratic equation. If \(\alpha\) is the minimum value of product of roots and \(\beta\) is the maximum value of sum of roots, then the sum of first six terms of geometric progression whose first term is \(\alpha\) and common ratio is \(\left(\frac{\alpha}{\beta}\right)\), is

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Completing the square for quadratic expressions in the form \(n^2 + bn + c\) is the fastest way to identify minimum or maximum values without using calculus.

Updated On: Apr 7, 2026

\(\frac{364}{243}\)
\(\frac{343}{243}\)
\(\frac{256}{81}\)
\(\frac{364}{81}\)

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The Correct Option is A

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