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The sum of roots of the equation x2 – |2x – 3| – 4 = 0 is.

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–2

\sqrt{2}

- \sqrt{2}

answer is D.

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Detailed Solution

x2 – |2x – 3| – 4 = 0
|2x – 3| = 2x – 3, when 2x – 3 > 0
For the above case, the equation becomes x2 – 2x – 1 = 0
is discarded since x should be greater than
The equation becomes x2 + 2x – 7 = 0

x = \frac{- 2 \pm \sqrt{4 + 7 \times 4}}{2} = - 1 \pm 2 \sqrt{2}

- 1 - 2 \sqrt{2}

is discarded because it's more than 3/2.
Sum of the roots obtained is

- 1 - 2 \sqrt{2} + 1 + \sqrt{2} = - \sqrt{2}

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