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_2a n d\ beta_1,beta_2 be the roots of a x^2+c=0\ a n d\ p x^2+q x+r=0 respectively. If the system of equations alpha_1, y+alpha_2z=0\ a n d\ beta_1y+beta_2z=0 has anon-trivial solution, then prove that (b^2)/(q^2)=(a c)/(p r)dot

Let alpha_(1),alpha_(2) and beta_(1),beta_(2) be the roots of 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_(2) z = 0 has a non - trivial solution, then a) b^(2) pr = q^(2) ac b) bpr^(2) = qac^(2) c) bp^(2)r = qa^(2)c d)None of these

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_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 and beta are the roots of the equation px^(2) + qx + 1 = , find alpha^(2) beta + beta^(2)alpha .

If alpha and beta are roots of the equation ax^2+bx+c =0 and, if px^2+qx+r =0 has roots (1-alpha)/alpha and (1-beta)/beta , then r is equal is