IF the ratio of the roots of equation `x^2+px+q=0` be `a:b` prove that,`p^2ab=q(a+b)^2` Hence, find the condition of equal roots of the given equation.

If the ratio of the roots of the equation px^(2) + qx + r=0 is a:b, then (ab)/(a+b)^(2) =

The ratio of the roots of the equation ax^2+bx+c=0 is r:1 Prove that, b^2r=ac(r+1)^2 and hence find the condition so that the two roots may be equal to each other.

If the ratio of the roots of the equation px^2+qx+r is a:b, then ab/(a+b)^2 =

If p and q are the roots of the equation x^2+px+q =0, then

If the ratio of the roots of the quadratic equation x^(2)-px+q=0 be 2:3, then prove that 6p^(2)=25q .

If the ratio of the roots of the quadratic equation x^(2)-px+q=0 be m:n, then prove that p^(2)mn=q(m+n)^(2) .

If the ratio of the roots of the equation x^2-px+q=0 be 1:2 , find the relation between p and q.

If the roots of the equation px^2+rx+r=0 are in the ratio a:b , prove that , p(a+b)^2=rab .

If , p , q are the roots of the equation x^(2)+px+q=0 , then