If the ratio of the roots of `ax^(2) +2bx+c=0` is same as the ratio of the `px^(2)+2qx +r= 0`, then prove that `(b^(2))/(ac)= (q^(2))/(pr)`

If alpha, beta are the roots of ax^(2)+2bx+c=0 and alpha +delta, beta + delta are those of Ax^(2)+2Bx+C=0 , then prove that (b^(2)-ac)/(B^(2)-AC)= ((a)/(A))^(2)

If sin theta, cos theta are the roots of ax^(2)+bx+c=0 then prove that b^(2)=a^(2)+2ac

One of the two real roots of the quadratic equation ax^(2)+bx+c=0 is three times the other. Then prove that b^(2)-4ac=(4ac)/(3)

If one root of the quadratic equation ax^(2)+bx+c= 0 is equal to the nth power of the order, then prove that (ac^(n))^((1)/(n+1)) + (a^(n)c)^((1)/(n+1))=-b

If the roots of the equation x ^(2) + 2 bx + c =0 are alpha and beta, then b ^(2) - c is equal to

If a, b are the roots of x^(2)+px+1=0 and c, d are the roots of x^(2)+qx+1=0 , show that q^(2)-p^(2)=(a-c)(b-c)(a+d) (b+d) .