Find the condition that the roots of the quadratic equation `x^2+px+q=0` should be both postitive

Find the condition that the roots of the quadratic equation x^2+px+q=0 should be both negative

Find the condition that the roots of the quadratic equation x^2+px+q=0 should be equal in magnitude and opposite in signs

Find the condition for which the roots of the quadratic equation ax^2+bx+c=0(ane0) are both positive

Find the condition for which the roots of the quadratic equation ax^2+bx+c=0(ane0) are both roots are zero.

Find the condition for which the roots of the quadratic equation ax^2+bx+c=0(ane0) are both negative

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

Find the condition that the equation x^3 - px^2 + qx -x = 0 should have its roots in G.P.