need help with pre calc hw

Question

Find all zeros of 4x^3-20x^2+31x-21

Enter the zeros separated by commas. Enter exact value, not decimal approximations please

Answer 1

zeros of 4x^3 -20x^2 +31x -21= (x-3)(4x^2-8x +7)

using decartes' rule of signs

possible 3 + zeros

no possible - zeros

try x=0,1,2,3 bingo

x=3 is the only real zero

2 imaginary zeros, they come in conjugate pairs

zeros are: 3, 1+.5isqr3, 1-.5isqr3