Multiple choice

Find the quadratic equation which has its root as 1 and -2.

  1. x2 - 3x + 2 = 0

  2. x2 - 3x - 2 = 0

  3. x2 - x + 2 = 0

  4. x2 + x - 2 = 0
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D Correct answer
Explanation

If roots are 1 and -2, the equation is (x - 1)(x + 2) = 0, which expands to x^2 + 2x - x - 2 = 0, or x^2 + x - 2 = 0.

AI explanation

A quadratic equation can be formed from its roots using the formula x2 - (sum of roots)x + (product of roots) = 0. For the roots 1 and -2, the sum is 1 + (-2) = -1 and the product is (1)(-2) = -2. Substituting these values gives x2 - (-1)x + (-2) = 0, which simplifies to x2 + x - 2 = 0. The result is x2 + x - 2 = 0.

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