Question:medium

If \(\alpha, \beta\) are the roots of the equation \(x^2 + 3x + k = 0\) and \(\alpha + 1/\beta\), \(\beta + 1/\alpha\) are the roots of the equation \(4x^2 + px + 18 = 0\) then k satisfies the equation

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When relating the roots of two different polynomials, Vieta's formulas (\(sum = -b/a\), \(product = c/a\)) are your primary tools. Start by finding an expression that involves only one unknown (like \(k\) in this case), which often comes from the product of the new roots.

Updated On: Mar 30, 2026

\(2x^2 - 13x + 20 = 0\)
\(x^2 - 5x + 6 = 0\)
\(2x^2 - 7x + 3 = 0\)
\(x^2 - 8x + 15 = 0\)

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The Correct Option is B

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