Question

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

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Answer 1

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\[\text { Let } p = \left| x \right|\]

\[ \Rightarrow p^2 + p - 6 = 0\]

\[ \Rightarrow p^2 + 3p - 2p - 6 = 0\]

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

\[ \Rightarrow p = - 3, 2\]

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

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

\[\text { Modulus can not be negative }, \]

\[ \therefore \left| x \right| = 2\]

\[ \Rightarrow x = \pm 2\]

\[ \Rightarrow x = 2 \text { or } - 2\]

\[\text { Sum of the roots of x is 0 }\]