According to the fundamental theorem of algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0 1 root 3 roots 4 roots 9 roots

3 roots, since the polynomial is of third degree.

This follows immediately from the zero product property: if , then either or . We have



from which it follows that



each of which admits only one solution.

Or, using the fundamental theorem of algebra, expanding we have a polynomial that is of third degree:



The theorem states that a polynomial will have up to distinct roots. In this case, it follows that there are exactly 3, since the solutions to the system above are all distinct.