Multiple choice

If $\alpha, \beta$ are the roots of the equation $2{x}^{2}+3x+7=0$, find $\cfrac { 1 }{ \alpha } +\cfrac { 1 }{ \beta } $

  1. $\cfrac{-3}{5}$
  2. $\cfrac{3}{7}$
  3. $\cfrac{-3}{7}$

  4. None
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C Correct answer
Explanation

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

AI explanation

Using the relationship between roots and coefficients for 2x squared + 3x + 7 equals 0, the sum of the roots alpha + beta is negative 3/2 and the product alpha beta is 7/2. We need to find 1/alpha + 1/beta, which combines to (alpha + beta) divided by (alpha beta). Substituting the values gives (negative 3/2) divided by (7/2), which simplifies to negative 3/7.

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