Multiple choice

If p, q, r are roots of the equation $(x-3)(x^2-9x-2018)=0$, then $p+q+r$ is?

  1. $12$
  2. $6$
  3. $-12$
  4. $-6$
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A Correct answer
Explanation

The equation is (x-3)(x^2-9x-2018) = 0. The roots are 3 and the roots of x^2-9x-2018=0. Let the roots be p, q, r. One root is 3. The sum of the other two roots from the quadratic is 9. Total sum = 3 + 9 = 12.

AI explanation

Expanding the given factored equation (x-3)(x^2-9x-2018) produces x^3 - 9x^2 - 2018x - 3x^2 + 27x + 6054, which simplifies to x^3 - 12x^2 - 1991x + 6054 = 0. Using Vieta's formulas, the sum of the roots p + q + r is found by taking the negative of the coefficient of the x^2 term. The sum of the roots is 12.

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