`alpha ` and `beta ` are the roots of `x^(2) - 5x - 1 = 0 ` . Complete the following activity to find the value of `x^(2) + beta^(3)`.

alpha and beta are the roots of x^2-3x-7=0 . Complete the following activity to find the value of alpha^3+ beta ^3 .

If alpha, beta are the roots of x^(2) - 3x + a = 0 , a in R and lt 1 lt beta, then find the values of a

If alpha, beta are the roots of x^(2) - 3x + a = 0 , a in R and lt 1 lt beta, then find the values of a

If alpha and beta are the roots of the equation 3x^(2) - 5x + 2 = 0 , then find the value of alpha^2beta + alphabeta^2 .

If alpha and beta are the roots of 2x^(2) + 5x - 4 = 0 then find the value of (alpha)/(beta) + (beta)/(alpha) .

If alpha, beta, 1 are the roots of x ^(3) - 2x ^(2) - 7x + 6 =0, then find alpha, beta.

Let alpha and beta be the roots of x^2 - 5x - 1 = 0 then find the value of (alpha^15 + alpha^11 + beta^15 + beta^11)/(alpha^13 + beta^13) .

If alpha and beta are the roots of the equation x^2+4x + 1=0(alpha > beta) then find the value of 1/(alpha)^2 + 1/(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,beta and 1 are the roots of x^(3)-2x^(2)-5x+6=0 then (alpha,beta)=