Determine the roots of the given polynomial. Give exact answers. f(x) = x4+4x3+8x2+8x+3

Answer 1

Possible rational,roots are 1,3,-1and -3

decartes rule of signs tell,you that there are no positive roots(no sign changes)

‘using synthetic division you get x=-1 as a solution twice

the remaining quadratic is x^+2x +3 . You can solve this using quadratic formula or completing the square which gives you -1 +i sqroot 2 and -1-i sqroot 2