[JEE Advanced 2010] let p q in mathbb r p 0 p 3 q if alpha beta
Let $p,q\in\mathbb R$, $p\ne0$, $p^3\ne\pm q$. If $\alpha,\beta$ (non-zero complex) satisfy $\alpha+\beta=-p$ and $\alpha^3+\beta^3=q$, then a quadratic with roots $\frac\alpha\beta,\frac\beta\alpha$ is
(a) $(p^3+q)x^2-(p^3+2q)x+(p^3+q)=0$
(b) $(p^3+q)x^2-(p^3-2q)x+(p^3+q)=0$
(c) $(p^3-q)x^2-(5p^3-2q)x+(p^3-q)=0$
(d) $(p^3-q)x^2-(5p^3+2q)x+(p^3-q)=0$
1 Answer
VAVidaara Admin
✓ Vidaara Team
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· 2d ago
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Correct answer: (b) $(p^3+q)x^2-(p^3-2q)x+(p^3+q)=0$
$\alpha\beta=\frac{p^3+q}{3p}$; $\frac\alpha\beta+\frac\beta\alpha=\frac{p^2-2\alpha\beta}{\alpha\beta}=\frac{p^3-2q}{p^3+q}$, product $1$. So $(p^3+q)x^2-(p^3-2q)x+(p^3+q)=0$.
JEE Advanced 2010 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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