Quadratic Equations

Quantitative Aptitude (CDS)

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If the equations x²- px + q=0 and x² + qx - p = 0 have a common root, then which one of the following is correct?

p − q = 0

p + q − 2 = 0

p + q − 1 = 0

p − q − 1 = 0

Explanation:

Here a= 1, b = − p, c = q and a' = 1, b' = q, c' = − p
Applying common root condition,
(a'c − ac')² = (bc' − b'c)(ab' − a'b)
=> (q + p)² = (p² − q² ) (q + p)
=> (p + q) = (p − q) (p + q)
=> p − q = 1
=> p − q − 1 = 0

By: Munesh Kumari

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