# For the Equation | X | 2 + | X | − 6 = 0 ,The Sum of the Real Roots is - Mathematics

MCQ

For the equation $\left| x \right|^2 + \left| x \right| - 6 = 0$ ,the sum of the real roots is

#### Options

• 1

• 0

• 2

• none of these

#### Solution

0

$\text { Let } p = \left| x \right|$

$\Rightarrow p^2 + p - 6 = 0$

$\Rightarrow p^2 + 3p - 2p - 6 = 0$

$\Rightarrow \left( p + 3 \right)\left( p - 2 \right) = 0$

$\Rightarrow p = - 3, 2$

$\text { Also }, \left| x \right| = p$

$\Rightarrow \left| x \right| = 2, or \left| x \right| = - 3$

$\text { Modulus can not be negative },$

$\therefore \left| x \right| = 2$

$\Rightarrow x = \pm 2$

$\Rightarrow x = 2 \text { or } - 2$

$\text { Sum of the roots of x is 0 }$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Q 2 | Page 16

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