Multiple choice

IF $\alpha$ and $\beta$ are the roots of the equation $3x^2 + x - 10 = 0$, then the value of $\dfrac{1}{\alpha} + \dfrac{1}{\beta}$ is.............

  1. 1
  2. $-\dfrac{1}{10}$
  3. $\dfrac{1}{10}$
  4. $\dfrac{1}{3}$
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C Correct answer
Explanation

For ax^2 + bx + c = 0, 1/alpha + 1/beta = (alpha + beta) / (alpha * beta). Here, alpha + beta = -b/a = -1/3 and alpha * beta = c/a = -10/3. Ratio = (-1/3) / (-10/3) = 1/10.

AI explanation

To find the value of (1/alpha) + (1/beta), combine the fractions to get (alpha + beta) / (alpha * beta). For the quadratic equation 3x^2 + x - 10 = 0, the sum of the roots alpha + beta equals -1/3 and the product of the roots alpha * beta equals -10/3. Substituting these values into the expression gives (-1/3) / (-10/3), which simplifies exactly to 1/10.

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