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Question
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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