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JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(p\) and \(q\) are non-zero real numbers and \({\alpha ^3} + {\beta ^3} = - p\), \(\alpha \beta = q\), then a quadratic equation whose roots are \(\frac{{{\alpha ^2}}}{\beta },\frac{{{\beta ^2}}}{\alpha }\) is
- A \(px^2 -qx + p^2 = 0\)
- B \(qx^2 + px + q^2 = 0\)
- C \(px^2 + qx+ p^2 =0\)
- D \(qx^2 -px + q^2 = 0\)
Answer & Solution
Correct Answer
(B) \(qx^2 + px + q^2 = 0\)
Step-by-step Solution
Detailed explanation
Given \(\alpha^{3}+\beta^{3}=-p\) and \(\alpha \beta=q\) Let \(\frac{\alpha^{2}}{\beta}\) and \(\frac{\beta^{2}}{\alpha}\) be the root of required quadratic equation. So, \(\frac{\alpha^{2}}{\beta}+\frac{\beta^{2}}{\alpha}=\frac{\alpha^{3}+\beta^{3}}{\alpha \beta}=\frac{-p}{q}\)…
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