[JEE Main 2009] if the roots of bx 2 cx a 0 are imaginary then for all
If the roots of $bx^2+cx+a=0$ are imaginary, then for all real $x$, the expression $3b^2x^2+6bcx+2c^2$ is
(a) less than $4ab$
(b) greater than $-4ab$
(c) less than $-4ab$
(d) greater than $4ab$
1 Answer
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· 2d ago
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Correct answer: (b) greater than $-4ab$
Imaginary roots $\Rightarrow c^2<4ab$. The minimum of $3b^2x^2+6bcx+2c^2$ is $-c^2>-4ab$, so it is greater than $-4ab$ for all $x$.
JEE Main 2009 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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