Sum of the real roots in the equation $x^{2} | x | - 17 x^{2} + 95 | x | - 175 = 0$ is:

None

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$34$

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$0$

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$17$

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Solution

The correct option is C
$0$

$x^{2} | x | - 17 x^{2} + 95 | x | - 175 = 0$

$\Rightarrow | x |^{3} - 17 | x |^{2} + 95 | x | - 175 = 0$

$\Rightarrow (| x | - 5) (| x |^{2} - 12 | x | + 35) = 0$

$\Rightarrow (| x | - 5) (| x | - 5) (| x | - 7) = 0$

$\Rightarrow | x | = 5, 5, | x | = 7$

$\Rightarrow$ Roots are $5, - 5, 5, - 5, 7, - 7$ whose sum $= 0$

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Sum of the real roots in the equation $x^{2} | x | - 17 x^{2} + 95 | x | - 175$ = 0 is:

x^{2} + | x | - 6 = 0

For the equation $| x^{2} | + | x | - 6 = 0$ , the roots are

x^{2} + 15 = 8 | x |

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