Question

given that root 2 is a zero of the cubic polynomial 6x3 +root 2 x2-10x -4root2 find other zeros

Answer 1

first of all as it is given that under root 2 is a root of the given cubic polynomial so let's take x minus root 2 is a factor of the given polynomial equation now if it is a factor it should divide that given cubic polynomial without leaving a reminder now divide this given cubic polynomial by x minus root 2 gives six x square + 7 root 2 x plus 4 now solve this quadratic equation by factorization method give the two factors that is X + 4 and under root 2 X + 1 now equate these two factors equal to zero gives us the two other zeros of the given cubic polynomial and that are minus 4 and minus one upon root 2