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 $2a^2+b^2=p^2+q^2$
• C. Two common roots if $3pq=2ab$
• D. Two common roots if $3bq=2ap$

Answer 1

The correct option is A

No common root

$2a^2{x}^2-2abx+b^2=0$
${\Delta }_1=4a^2{b}^2-8a^2{b}^2$
$\Rightarrow {\Delta }_1<0$

$p^2{x}^2+2pqx+q^2=0{\Delta }_2=4p^2{q}^2=4p^2{q}^2=0\Rightarrow {\Delta }_2=0$

$\therefore$ No common root