Multiple choice

Find the sum of square of the roots of the equation x2 + 5x - 6 = 0.

  1. 13

  2. 19

  3. 27

  4. 37
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D Correct answer
Explanation

For x^2 + 5x - 6 = 0, roots alpha and beta satisfy alpha+beta = -5 and alpha*beta = -6. alpha^2 + beta^2 = (alpha+beta)^2 - 2*alpha*beta = (-5)^2 - 2(-6) = 25 + 12 = 37.

AI explanation

For the equation x2 + 5x - 6 = 0, the sum of the roots is -b/a = -5 and the product of the roots is c/a = -6. The sum of the squares of the roots is calculated using the identity (sum of roots)2 - 2(product of roots). Substituting the values gives (-5)2 - 2(-6) = 25 + 12 = 37. The result is 37.

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