[JEE Main 2002] if alpha beta but alpha 2 5 alpha 3 and beta 2 5 beta
If $\alpha\ne\beta$ but $\alpha^2=5\alpha-3$ and $\beta^2=5\beta-3$, then the equation having $\frac\alpha\beta$ and $\frac\beta\alpha$ as roots is
(a) $3x^2-19x+3=0$
(b) $3x^2+19x-3=0$
(c) $3x^2-19x-3=0$
(d) $x^2-5x+3=0$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (a) $3x^2-19x+3=0$
$\alpha,\beta$ are roots of $x^2-5x+3=0$, so $\alpha+\beta=5,\alpha\beta=3$. Then $\frac\alpha\beta+\frac\beta\alpha=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{19}3$ and product $=1$: $3x^2-19x+3=0$.
JEE Main 2002 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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