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_2z=0` and `beta_1y_beta_2z=0` has a non trivial solution then prove that `b^2/q^2=(ac)/(pr)`

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_(1)y+alpha_(2)z=0 and beta_(1)y_(beta-)2z=0 has a non trivial solution then prove that (b^(2))/(q^(2))=(ac)/(pr)

If alpha_1, alpha_2 be the roots of equation x^2+px+q=0 and beta_1,beta be those of equation x^2+rx+s=0 and the system of equations alpha_1y+alpha_2z=0 and beta_1 y+beta_2 z=0 has non trivial solution, show that p^2/r^2=q/s

If alpha. beta are roots of the equation ax^(2)+bx+c=0 and alpha-beta=alpha*beta then

If alpha and beta be the roots of the equation ax^(2)+bx+c=0 then equation whose roots are alpha+beta and alpha beta is