If alpha and beta be the roots of equation x^2-x+1=0, then alpha^2009 + beta^2009 is equal to? [Ans: 1]. if alpha and beta are the roots of the equation x2-x 1=0 then alpha power 2009 beta power 2009 . Tags: Class 11 , Maths , Binomial Theorem Asked by krishna Murari. If alpha and beta are the roots of the equation x2 - x + 1 = 0, then alpha 2009 + beta 2009 = Show transcribed image text If alpha and beta are the roots of the equation x2 - x + 1 = 0, then alpha 2009 + beta 2009 = Expert Answer. 100 %(1 rating) This problem has been solved! See the answer . Previous question Next question . x^2+4x-6=0 with roots ALPHA, Beta. Find equation for roots ALPHA^2 + BETA and BETA^2 + ALPHA. I feel like i'm so lost when the roots change from beta^2 or alpha^3 or when is 1/(over)b^2 etc Find equation for roots ALPHA^2 + BETA and BETA^2 + ALPHA.. Here,Let. a*sqrt(x) + b*x + c = 0 be a quadratic equation. Now,Let. alpha , beta be the roots of the quadratic equation (Since only 2 roots can exist for a quadratic equation). #Q.1# If #alpha,beta# are the roots of the equation #x^2-2x+3=0# obtain the equation whose roots are #alpha^3-3 alpha^2+5 alpha -2# and #beta^3-beta^2+beta+5#?.