For the polynomial given below you are given one of its zero

For the polynomial given below, you are given one of its zeros. Use the techniques in this section to find the rest of the real zeros. (Enter your answers as a comma-separated list. If there are no other zeros, enter the zero given.)

For the polynomial given below, you are given one of its zeros. Use the techniques in this section to find the rest of the real zeros. (Enter your answers as a comma-separated list. If there are no other zeros, enter the zero given.)

x=

Factor the polynomial.

Solution

f(x)= x²-2x-2 ,x=1-sqrt 3

to find the other root we have to divide f(x) by x-1+sqrt3

(x²-2x-2)/(x-1+sqrt3) = x-1-sqrt3

so we can write f(x)= (x-1-sqrt3)(x-1+sqrt3)