Multiple choice

The sum of the roots of the equation, $x^2-|2x-3|-4=0$ is

  1. $2$
  2. $-2$
  3. $\sqrt 2$
  4. $-\sqrt 2$
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D Correct answer
AI explanation

For the equation x^2 - |2x - 3| - 4 = 0, we consider two cases based on the absolute value. When x is greater than or equal to 1.5, the equation becomes x^2 - (2x - 3) - 4 = 0, which simplifies to x^2 - 2x - 1 = 0; solving this gives x = 1 plus the square root of 2. When x is less than 1.5, the equation becomes x^2 - (-2x + 3) - 4 = 0, or x^2 + 2x - 7 = 0; solving this yields x = -1 minus twice the square root of 2. The sum of these valid roots is 1 plus the square root of 2 plus negative 1 minus twice the square root of 2, which simplifies to negative the square root of 2.

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