Question

Alpha,beta,gama are the zeros of polynomial 6x 3 +3x 2 -5x+1,then find alpha -1 +beta -1 +gama -1

Answer 1

since alpha,beta, gamma are zeroes of polynomial 6x^3 + 3x^2 - 5x + 1
so alpha + beta + gamma = -3/6 = -1/2 ( since sum of the zeroes of a cubic polynomial ax^3 + bx^2 + cx + d is -b/a ) 
so alpha -1 + beta -1 + gamma - 1  = (alpha + beta + gamma) - 3                                                                           = -1/2 - 3   
                                                        = - 7/2