Multiple choice

For the equation x2 + |x| - 6 = 0, analyse the four statements below for correctness.

  1. There is only one root.

  2. Sum of the roots is +1.

  3. Sum of the roots is zero.

  4. The product of the roots is +4.
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C Correct answer
Explanation

x^2 + |x| - 6 = 0. If x >= 0, x^2 + x - 6 = 0 => (x+3)(x-2)=0 => x=2. If x < 0, x^2 - x - 6 = 0 => (x-3)(x+2)=0 => x=-2. Roots are 2, -2. Sum = 0.

AI explanation

Because |x|^2 is identical to x^2 for all real numbers, the equation can be rewritten as |x|^2 + |x| - 6 = 0. Treating |x| as a single variable yields the factors (|x| + 3)(|x| - 2) = 0, giving |x| = 2 since |x| cannot be negative. This produces two roots, x = 2 and x = -2, making the sum of the roots zero.

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