Multiple choice

If $\alpha$ and $\beta$ are the roots of the quadratic equation $4x^2+3x+7=0$, then the value of $\displaystyle\frac{1}{\alpha}+\frac{1}{\beta}$ is:

  1. $-\displaystyle\frac{3}{4}$
  2. $-\displaystyle\frac{3}{7}$
  3. $\displaystyle\frac{3}{7}$
  4. $\displaystyle\frac{4}{7}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 4x^2 + 3x + 7 = 0, sum of roots alpha + beta = -3/4 and product alpha*beta = 7/4. The expression 1/alpha + 1/beta = (alpha + beta) / (alpha*beta) = (-3/4) / (7/4) = -3/7.

AI explanation

To find the value of 1/alpha + 1/beta, we first combine the fractions to get (alpha + beta) / (alpha * beta). Using Vieta's formulas for the equation 4x^2 + 3x + 7 = 0, the sum of the roots alpha + beta equals -3/4 and the product alpha * beta equals 7/4. Dividing the sum by the product gives (-3/4) / (7/4) = -3/7.

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