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

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

If alpha and beta are the zeroes of the polynomial 2x^2 + 5x + 1 , then the value of alpha +beta+ alpha beta is

Let alpha , beta be roots of x^(2) + x +1 = 0 , then the equation whose roots are (alpha)^10 and (beta)^13 is

If alpha and beta are roots of the equation x^(2) + 2x + 8 = 0 the the value of (alpha)/(beta) + (beta)/(alpha) is ………….. .

If alpha and beta are the roots of the equation x^2 + 2x +8=0 then the value of (alpha)/(beta) + (beta)/(alpha) is ………………….. .

If alpha,beta be the roots of x^(2)-a(x-1)+b=0 , then the value of (1)/(alpha^(2)-a alpha)+(1)/(beta^(2)-a beta)+(2)/(a+b) is

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 are the roots of x^2 +x+1=0 then alpha beta + beta alpha =