If `alpha,beta` are the roots of the equation `x^2 + px + q = 0`, then `-1/alpha,-1/beta` are the roots of the equation.

If alpha,beta are the roots of the equation x^(2)-px+q=0 and alpha_(1),beta_(1) be the roots of the equation x^(2)-qx+p=0, then form the quadratic equation whose roots are (1)/(alpha_(1)beta)+(1)/(alpha beta_(1)) and (1)/(alpha_(1)alpha)+(1)/(beta beta_(1))

If alpha and beta are roots of the equation x^(2)+px+2=0 and (1)/(alpha)and (1)/(beta) are the roots of the equation 2x^(2)+2qx+1=0 , then (alpha-(1)/(alpha))(beta-(1)/(beta))(alpha+(1)/(beta))(beta+(1)/(alpha)) is equal to :

Let alpha, beta in R. If alpha, beta^(2) are the roots of quadratic equation x^(2) - px + 1 = 0 and alpha^(2), beta are the roots of quadratic equation x^(2) -px + 8 = 0 , then find p, q , alpha, beta .

If alphaandbeta are the roots of the equation x^(2)+px+q=0 , then -alpha^(-1),-beta^(-1) are the root of which one of the following equations?

If (alpha+sqrt(beta)) and (alpha-sqrt(beta)) are the roots of the equation x^(2)+px+q=0 where alpha,beta,p and q are real,then the roots of the equation (p^(2)-4q)(p^(2)x^(2)+4px)-16q=0 are

If alpha,beta are the roots of the equation x^(2) + Px + P^(3) = 0, P ne 0 such that alpha =beta^(2) then the roots of the given equation are

If alpha,beta are the roots of the equation x^(2) + Px + P^(3) = 0, P ne 0 such that alpha =beta^(2) then the roots of the given equation are

IF alpha,beta be the roots of the equation x^2+px+q=0 , show that 1/(alpha+beta) and 1/alpha+1/beta are the roots of pqx^2+(p^2+q)x+p=0

If alpha and beta are the roots of the equation x^(2) + px + q =0, then what is alpha ^(2) + beta ^(2) equal to ?