If `alpha & beta ` are the roots of the equation `a x^2 + b x + c = 0,` then `(1 + alpha + alpha^2) (1 + beta + beta^2) =`

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

If alpha, beta are the roots of the equation x^(2) + x + 1 = 0 then prove that alpha^(4) + beta^(4) + alpha^(-1) beta^(-1) = 0 .

If alpha,beta are the roots of the equation x^(2)-p(x+1)-c=0, then (alpha+1)(beta+1)=

If alpha,beta " are the roots of the equation "x^(2) - 2x - 1 =0, "then what is the value of " alpha^(2)beta^(-2)+alpha^(-2)beta^(2)

If alpha and beta are the roots of the equation 3x^(2) - 5x + 2 = 0 , find the value of (i) (alpha)/(beta) + (beta)/(alpha) (ii) alpha-beta (iii) (alpha^(2))/(beta) + (beta^(2))/(alpha)

If alpha and beta be the roots of equation x^(2) + 3x + 1 = 0 then the value of ((alpha)/(1 + beta))^(2) + ((beta)/(1 + alpha))^(2) is equal to