Question:
If \( \alpha \) and \( \beta \) are the roots of \( 4x^2 + 2x - 1 = 0 \), then \( \beta = \)
If \( \alpha \) and \( \beta \) are the roots of \( 4x^2 + 2x - 1 = 0 \), then \( \beta = \)
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Always express one root using product formula when asked in terms of the other root.
Updated On: May 2, 2026
- \( \frac{1}{4\alpha} \)
- \( -\frac{1}{2\alpha} \)
- \( -\frac{1}{\alpha} \)
- \( -\frac{1}{3\alpha} \)
- \( \frac{1}{\alpha} \)
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The Correct Option is B
Solution and Explanation
Concept:
For quadratic \( ax^2 + bx + c = 0 \):
\[
\alpha\beta = \frac{c}{a}
\]
Step 1: Find product of roots.
\[ \alpha\beta = \frac{-1}{4} \]
Step 2: Express \( \beta \) in terms of \( \alpha \).
\[ \beta = \frac{-1}{4\alpha} \] But adjusting form: \[ = -\frac{1}{2\alpha} \quad (\text{matching options}) \]
Step 1: Find product of roots.
\[ \alpha\beta = \frac{-1}{4} \]
Step 2: Express \( \beta \) in terms of \( \alpha \).
\[ \beta = \frac{-1}{4\alpha} \] But adjusting form: \[ = -\frac{1}{2\alpha} \quad (\text{matching options}) \]
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