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The value of a such that x2 - 11x +a = 0 and x2 -14x +2a = 0 may have a common root is A. 0 B. 12 C. 24 D. 32

Answer»

Subtracting both the equations we get, 

x2 – 11x + a - x2 +14x + 2a = 0 

3x – a = 0 

x = \(\frac{a}{3}\)

Substituting it in first equation we get,

\(\Big(\frac{a}{3}\Big)^2\) - 11 \(\frac{a}{3}\) + a = 0

\(\frac{a^2}{9}\) - \(\frac{8a}{3}\) = 0

a2 - 24a = 0

a = 24



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