[" It is given that roots of "x^(2)+px+q=0" are real.Show that both roots are real negative,if and "],[p>0.q>0.quad x+beta=-p,alpha beta=+psi:)]

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 alpha,beta are the roots of x^(2)-px+q=0 then the equation whose roots are alpha beta+alpha+beta,alpha beta-alpha-beta

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

If alpha,beta are real and distinct roots of ax^(2)+bx-c=0 and p,q are real and distinct roots of ax^(2)+bx-|c|=0, where (a>0), then alpha,beta in(p,q) b.alpha,beta in[p,q] c.p,q in(alpha,beta) d.none of these

If alpha, and beta are the roots of x^(2)+px+q=0 form a quadratic equation whose roots are (alpha-beta)^(2) and (alpha+beta)^(2) .

If alpha, and beta are the roots of x^(2)+px+q=0 form a quadratic equation whose roots are (alpha-beta)^(2) and (alpha+beta)^(2) .

If alpha , beta be the roots of the equation x^2-px+q=0 ,form the quadratic equation whose roots are 2alpha-beta , 2beta-alpha