Multiple choice

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + 3x - 4 = 0$, then $\dfrac{1}{\alpha} + \dfrac{1}{\beta}$ is equal to

  1. $\dfrac{-3}{4}$
  2. $\dfrac{3}{4}$
  3. $\dfrac{-4}{3}$
  4. $\dfrac{4}{3}$
  5. $\dfrac{3}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For x^2 + 3x - 4 = 0, sum of roots alpha + beta = -3, product alpha * beta = -4. 1/alpha + 1/beta = (alpha + beta) / (alpha * beta) = -3 / -4 = 3/4.

AI explanation

For the equation x^2 + 3x - 4 = 0, Vieta's formulas state that the sum of the roots (alpha + beta) is -3 and the product (alpha*beta) is -4. The expression 1/alpha + 1/beta can be combined over a common denominator to equal (alpha + beta) / (alpha*beta). Substituting the values from Vieta's formulas gives (-3) / (-4), which equals 3/4.

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