Let $\alpha_1,\alpha_2$ and $\beta_1,\beta_2$ be the roots of the equation $ax^2+bx+c=0$ and $px^2+qx+r=0$ respectively.If the system of equations $\alpha_1y+\alpha_2 z=0$ and $\beta_1 y+\beta_2 z=0$ has a non trivial solution then prove that $b^2/q^2=ac/pr$?
Ok I can find sum of roots of first and second equation individually.But for the system to have non trivial solution $(\alpha_1\beta_2-\alpha_2\beta_1)=0$.Now how do I get to this?
HINT:
$\implies\dfrac{\alpha_1}{\beta_1}=\dfrac{\alpha_2}{\beta_2}=k$(say)
Find $$\dfrac{\beta_1+\beta_2}{\alpha_1+\alpha_2}$$ and $$\dfrac{\beta_1\beta_2}{\alpha_1\alpha_2}$$