Question

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

• A. No common root
• B. One common root if
• C. Two common roots if 3pq = 2ab
• D. Two common roots if 3bq = 2ap

Answer 1

The correct option is A

No common root

$2a^2{x}^2-2abx+b^2=0$ $\Rightarrow$ ${\Delta }_1$< 0

$p^2{x}^2+2pqx+q^2=0$ $\Rightarrow$ ${\Delta }_2=0$

$\therefore$ no common root