Multiple choice

If + 2 and - 3 are the roots of a quadratic equation, the equation will be _______.

  1. x 2 - x + 6 = 0

  2. x 2 + x - 5 = 0

  3. x 2 - x - 6 = 0

  4. x 2 + x - 6 = 0
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D Correct answer
Explanation

If roots are r1 and r2, the equation is (x - r1)(x - r2) = 0. (x - 2)(x + 3) = x^2 + 3x - 2x - 6 = x^2 + x - 6 = 0.

AI explanation

To form a quadratic equation from its roots, we use the standard formula x2 - (sum of roots)x + (product of roots) = 0. Here, the sum of the roots 2 and -3 is -1, and their product is -6. Substituting these values gives the equation x2 - (-1)x + (-6) = 0, which simplifies to x2 + x - 6 = 0. The result is x2 + x - 6 = 0.

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