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CAT 2019 Quant Question with Solution 33

The number of solutions to the equation $|x|\left(6 x^{2}+1\right)=5 x^{2}$ is

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Correct Answer: 5

case I: x=0.

Clearly, $x=0$ satisfy the equation.

case II: x>0

$|x|\left(6 x^{2}+1\right)=5 x^{2}$

$\Rightarrow x\left(6 x^{2}+1\right)=5 x^{2}$

$\Rightarrow 6 x^{2}+1-5 x=0$

On solving the quadratic equation, we get $x=\frac{1}{2},\frac{1}{3}$ (both valid)

Case III: x<0

$|x|\left(6 x^{2}+1\right)=5 x^{2}$

$\Rightarrow \quad-x\left(6 x^{2}+1\right)=5 x^{2}$

$\Rightarrow \quad 6 x^{2}+5 x+1=0$

On solving the quadratic equation, we get $x=\frac{-1}{2}\text{ ,}\frac{-1}{3}$ (both valid)

Hence there are 5 solutions.

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