Multiple choice

Find the sum of the reciprocals of the roots of the equation $x^2+ px + q = 0$.

  1. $-\dfrac{p}{q}$
  2. $\dfrac{q}{p}$
  3. $\dfrac{p}{q}$
  4. $-\dfrac{q}{p}$
  5. $p+q$
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A Correct answer
Explanation

For x^2 + px + q = 0, sum of roots alpha + beta = -p, product alpha * beta = q. The sum of reciprocals is 1/alpha + 1/beta = (alpha + beta) / (alpha * beta) = -p / q.

AI explanation

Using Vieta's formulas for the quadratic equation x^2 + px + q = 0, the sum of the roots is -p and the product of the roots is q. The sum of the reciprocals of the roots can be written as 1/alpha + 1/beta. By combining these fractions over a common denominator, we get (alpha + beta) / (alpha * beta). Substituting the values from Vieta's formulas yields -p/q.

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