Question:
If the equations \( x^2 + px + 12 = 0 \), \( x^2 + qx + 15 = 0 \), and \( x^2 + (p+q)x + 36 = 0 \) have a common positive root, then what is the value of \( (2p - q) \)?
If the equations \( x^2 + px + 12 = 0 \), \( x^2 + qx + 15 = 0 \), and \( x^2 + (p+q)x + 36 = 0 \) have a common positive root, then what is the value of \( (2p - q) \)?
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For problems involving common roots, equate the discriminants and solve for the unknowns.
Updated On: Apr 17, 2025
- \( -6 \)
- \( -5 \)
- \( 5 \)
- \( 7 \)
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The Correct Option is A
Solution and Explanation
Since all three equations have a common root, solve the system of equations by setting the discriminants equal. Use the common root to find the values of \( p \) and \( q \), then calculate \( 2p - q \).
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