The roots `alpha and beta` of the quadratic equation `ax^(2)+bx+c=0` are and of opposite sing. The roots of the equation `alpha(x-beta)^(2)+beta(x-alpha)^(2)=0` are

The roots alpha and beta of the quadratic equation px^(2) + qx + r = 0 are real and of opposite signs. The roots of alpha(x-beta)^(2) + beta(x-alpha)^(2) = 0 are:

Let alpha,beta be the roots of the quadratic equation ax^2+bx+c=0 then the roots of the equation a(x+1)^2+b(x+1)(x-2)+c(x-2)^2=0 are:-

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

If alpha, beta are the roots of the quadratic equation ax^(2)+bx+c=0, form a quadratic equation whose roots are alpha^(2)+beta^(2) and alpha^(-2) + beta^(-2) .

If alpha and beta are roots of the quadratic equation x ^(2) + 4x +3=0, then the equation whose roots are 2 alpha + beta and alpha + 2 beta is :

If alpha and beta are the roots of the quadratic equation ax^(2)+bx+1 , then the value of (1)/(alpha beta)+(alpha+beta) is

If alpha and beta are the roots of the quadratic equation ax^(2)+bx+1 , then the value of 2alpha^(2)beta^(2) is

If alpha, beta are the roots of the equation ax^(2) +2bx +c =0 and alpha +h, beta + h are the roots of the equation Ax^(2) +2Bx + C=0 then

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

Two different real numbers alpha and beta are the roots of the quadratic equation ax ^(2) + c=0 a,c ne 0, then alpha ^(3) + beta ^(3) is: