Question

Obtain all the zeroes of the polynomial x4 - 7x3 + 17x2 - 17x + 6 if two of its zeroes are 1 and 2
answer in brief

Answer 1

since 1 and 2 are zeroes of the polynomial ( x-1)(x-2) is a factor of given fourth degree polynomial so divide the given polynomial with x2-3x+2 then we get quotient as x2-4x+3 equate this to zero we get 1 and 3 as other zeroes of the polynomial hence the zeroes of the polynomial is 1,1,2,3