Multiple choice

For the cubic equation x3 + 6x2 - 37x - 210 = 0, find the sum of the squares of its roots.

  1. 90

  2. 105

  3. 110

  4. 125

  5. 127
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C Correct answer
Explanation

For x^3 + 6x^2 - 37x - 210 = 0, let roots be a, b, c. Sum of roots (a+b+c) = -6. Sum of roots taken two at a time (ab+bc+ca) = -37. The sum of squares of roots is (a+b+c)^2 - 2(ab+bc+ca) = (-6)^2 - 2(-37) = 36 + 74 = 110.

AI explanation

Using Vieta's formulas for the cubic equation x cubed plus 6 x squared minus 37 x minus 210 equals 0, the sum of the roots is negative 6 and the sum of the products of the roots taken two at a time is negative 37. The sum of the squares of the roots equals the square of the sum of the roots minus twice the sum of the products taken two at a time. Calculating this gives negative 6 squared minus 2 times negative 37, which is 36 plus 74, resulting in 110.

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