Question:
If the product of roots of the equation \( mx^2 + 6x + (2m - 1) = 0 \) is \( -1 \), then the value of \( m \) is:
If the product of roots of the equation \( mx^2 + 6x + (2m - 1) = 0 \) is \( -1 \), then the value of \( m \) is:
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Always check that \( m \neq 0 \), otherwise the equation is no longer quadratic.
Updated On: May 1, 2026
- \( \frac{1}{3} \)
- \( 1 \)
- \( 3 \)
- \( -1 \)
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The Correct Option is A
Solution and Explanation
Concept: For a quadratic equation \( ax^2 + bx + c = 0 \), the product of roots is: \[ \alpha \beta = \frac{c}{a} \]
Step 1: Identify coefficients clearly.
Given equation: \[ mx^2 + 6x + (2m - 1) = 0 \] Comparing with standard form: \[ a = m, \quad c = 2m - 1 \] So, product of roots: \[ \alpha \beta = \frac{2m - 1}{m} \]
Step 2: Use the given condition.
It is given that product of roots is \( -1 \), so: \[ \frac{2m - 1}{m} = -1 \]
Step 3: Solve the equation.
Multiply both sides by \( m \): \[ 2m - 1 = -m \] \[ 2m + m = 1 \] \[ 3m = 1 \] \[ m = \frac{1}{3} \]
Step 4: Final answer.
\[ \boxed{m = \frac{1}{3}} \]
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