[" 24.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 the roots of the equation px^(2)+qx+r=0 are in the ratio l:m then

In the equation px^2+rx+r=0 ratio of the roots are a:b then prove that p(a+b)^2=rab

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then prove that, 2p^3 −9pq+27r=0

If one of the root of the equation px^2 + qx + r = 0 is the cube of the other, prove that. rp(r + p)^2 = (q^2 - 2rp)^2 .

If alpha,beta are the roots of the equation px^(2)-qx+r=0, then the cquation whose roots are alpha^(2)+(r)/(p) and beta^(2)+(r)/(p) is

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

If the ratio of the roots of the equation x^(2)+px+q=0 are equal to ratio of the roots of the equation x^(2)+bx+c=0, then prove that p^(2c)=b^(2)q

IF one root of the equation px^2+qx+r=0 is the cube of the other, prove that , rp(r+p)^2=(q^2-2rp)^2 .

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) .