It is given that roots of `x^2+px+q=0` are real. Show that both roots are real negative,if and only if `p>0. q> 0.`

If all the roots of x^(3)+px+q=0p,q in R,q!=0 are real then

Show that the roots of the equation x^(2)+px-q^(2)=0 are real for all real values of p and q.

If all the roots of x^3 + px + q = 0 p,q in R,q != 0 are real, then

If the roots of the equation qx^2 + 2px + 2q =.0 are real and unequal then prove that the roots of the equation (p + q)x^2 + 2qx + (p - q)=0 are imaginary,

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

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

IF the roots of the equation px^2-2qx+p=0 are real and unequal, show that the roots of the equation qx^2-2px+q=0 are imaginary (both p and q are real).