Question:
If \(\alpha\) and \(\beta\) are roots of \(4x^2 + 3x + 7 = 0\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is
If \(\alpha\) and \(\beta\) are roots of \(4x^2 + 3x + 7 = 0\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is
Show Hint
Use sum and product of roots for such expressions.
Updated On: Apr 15, 2026
- -3/4
- 3/7
- -3/7
- 4/7
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
\[
\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha+\beta}{\alpha\beta}
\]
Step 1: Use relations.
\[ \alpha+\beta = -\frac{3}{4}, \quad \alpha\beta = \frac{7}{4} \]
Step 2: Compute.
\[ \frac{1}{\alpha} + \frac{1}{\beta} = \frac{-3/4}{7/4} = -\frac{3}{7} \]
Step 1: Use relations.
\[ \alpha+\beta = -\frac{3}{4}, \quad \alpha\beta = \frac{7}{4} \]
Step 2: Compute.
\[ \frac{1}{\alpha} + \frac{1}{\beta} = \frac{-3/4}{7/4} = -\frac{3}{7} \]
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