Find the rational zeros and then the other zeros of the poly

Find the rational zeros and then the other zeros of the polynomial function f(x) = x^3 - 11x^2 + 21x + 49, that is, solve f(x) = 0. Factor f(x) into linear factors. (a) Select the correct choice below and fill in any answer box(es) within your choice. (Type an exact answer, using radicals as needed. Simplify your answer. Use a comma to separate answers as needed.) There is only one rational zero. 7, and the other zeros are 2 + Squareroot 11.2 - Squareroot 11. There are only rational zeros and they are. There are no rational zeros. The other zeros are. (b) The factorization of f(x) into linear factors is (x-7). (Type an exact answer, using radicals as needed Simplify your answer Type an expression using x as the variable.)

Solution

x³-11x²+21x+49=0

(x-7)(x²-4x-7)=0

x-7=0 , x²-4x-7=0

x=7, x=2+-sqrt11

x=7, x=2+SQRT11,2-SQRT11