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 difference of the roots of the quadratic equation x^(2)-px+q=0 be 1, then prove that p^(2)+4q^(2)=(1+2q)^(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 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 equations x^(2) + px +q=0 is 3 times the other , prove that 3p^(2) = 16q.

In the equation x^2-px+q=0 ratio of the roots are 2:3 ,then prove that 6p^2=25q

If p and q are the roots of the quadratic equation x^(2)+px-q=0 , then find the values of p and q.

If the sum of the two roots of the quadratic equation x^2-px+q=0 be the thrice of their difference then prove that 2p^2=9q

Let p, q in R . If 2- sqrt3 is a root of the quadratic equation, x^(2)+px+q=0, then