If the quadratic equation $\left(b^2+c^2\right) x^2-2(a+b) c x+\left(c^2+a^2\right)=0$ has equal roo

Question

If the quadratic equation $\left(b^2+c^2\right) x^2-2(a+b) c x+\left(c^2+a^2\right)=0$ has equal roots, then

Professor PC Thomas Classes · Answer

$ \begin{aligned} & D=4(a+b)^2 c^2-4\left(c^2+a^2ight)\left(b^2+c^2ight) \ & 2 a b c^2=c^4+a^2 b^2 \ & \left(c^2-a bight)^2=0, c^2=a b \end{aligned} $