Question

If p, q, r are non-zero real numbers, the two equation, $2a^{2}x^{2}-2abx + b^{2} = 0$ and $p^{2}x^{2}+3pqx + q^{2} = 0$ have :

• A. no common root
• B. one common root if $2a^2+b^2 = p^2 + q^2$
• C. two common roots if $3pq = 2ab$
• D. two common roots if $3qb = 2\, ap$

Answer 1

Answer: (A)

Discriminant of the equation
$2a^{2}x^{2}-2abx + b^{2} = 0$ is $-4a^{2}b^{2} < 0$ and that of the equation
$p^{2}x^{2}+3pqx + q^{2} = 0$ is $5p^{2}q^{2} > 0$
There cannot be any common root.