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  4. The number of solutions of the equation x2 - 5 | x | + 6 = 0 is

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Q. The number of solutions of the equation $x^2 - 5 | x | + 6 = 0$ is

COMEDKCOMEDK 2006Complex Numbers and Quadratic Equations

Solution:

$x^2 - 5 | x | + 6 = \begin{cases} x^2 - 5 x + 6 = 0, & , x \geq 0\\ x^2 + 5x + 6 = 0 &, x < 0 \end{cases}$
$ \therefore $ Number of solutions of equation is 4