If $\displaystyle a,b,c \in R$ such that $\displaystyle abc \neq0$ If $\displaystyle x_1$ is a root of $\displaystyle a^2x^2+bx+c=0, x_2$ is a root of $\displaystyle a^2x^2-bx-c=0$ and $\displaystyle x_1 > x_2 >0$ then the equation $\displaystyle a^2x^2+2bx+2c=0$ has roots $\displaystyle x_3$ .
Prove that $\displaystyle x_3$ lies between $\displaystyle x_1 \& x_2$
Let f(x) = $\displaystyle a^2x^2+2bx+2c=0$