Question

The common root of two equations $(p^2-\sqrt{p+q}+r^2)x^2+(\sqrt{p+q}-r^2-1)x+(1-p^2)=0$ and $m^2{x}^2-(r^2+m^2)x+r^2=0$ is

• A. \N
• B. $\frac{1-p^2}{r^2}$
• C. $\frac{p^2+r^2-m^2}{\sqrt{p+q}}$
• D. none of these

Answer 1

The correct option is D none of these

$(p^2-\sqrt{p+q}+r^2)x^2+(\sqrt{p+q}-r^2-1)x+(1-p^2)=0$
$(p^2+r^2-\sqrt{p+q})x^2+(-p^2-r^2+\sqrt{p+q}+p^2-1)x+(1-p^2)=0$
$(p^2+r^2-\sqrt{p+q})x[x-1]+(p^2-1)(x-1)=0$
$(x-1)\left[\right(p^2+r^2-\sqrt{p+q})x+(p^2-1\left)\right]=0$
$m^2{x}^2-(r^2+m^2)x+r^2=0$
$x{m}^2(x-1)-r^2(x-1)=0$
$(m^{2}x-r^2)(x-1)=0$
Common root
x=1