If the equation, `x^2+3x+6=0` has roots `alpha, beta`, then find the equation having roots `alpha+beta, alpha-beta` is.

If alpha and beta the roots of the equation x^(2) + 9x + 18 = 0 , then the quadratic equation having the roots alpha + beta and alpha - beta is "_____" . Where (alpha gt beta) .

If the equation 3x^(2) - 2x-3 = 0 has roots alpha , and beta then alpha.beta = "______" .

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 equation 3x^(2)-5x+3 =0 , then the quadratic equation whose roots are alpha^(2)beta and alphabeta^(2) is :

If alpha and beta are the roots of the equation x^2 - 10x + 5 = 0 , then equation whose roots are (alpha+beta)^2 and (alpha-beta)^2 is

If alpha, beta are the roots of the equation x^2-bx+c=0 then find the equation whose roots are (alpha^2+beta^2)(alpha^3+beta^3) and alpha^5 beta^3+alpha^3beta^5-2alpha^4beta^4

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