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If a, b, p, q are non-zero real numbers, then the two equations $2 a^{2} x^{2} - 2 a^{2} x^{2} - 2 abx + b^{2} = 0 and p^{2} x^{2} + 2 pqx + q^{2} = 0$ have

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one common root if $2 a^{2} + b^{2} = p^{2} + q^{2}$

no common root

two common roots if 3bq = 2ap

two common roots if 3pq = 2ab

answer is A.

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Detailed Solution

$\begin{array}{l} 2 a^{2} x^{2} - 2 abx + b^{2} = 0 \Rightarrow Δ_{1} < 0 \\ p^{2} x^{2} + 2 pqx + q^{2} = 0 \Rightarrow Δ_{2} < 0 \\ ∴ no common root \end{array}$

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