SOLUTION: Find the possible rational zeros and then find all the zeros of the polynomial function: f(x)=x⁴+8x³+19x²+12x-2

Question 1177951: Find the possible rational zeros and then find all the zeros of the polynomial function: f(x)=x⁴+8x³+19x²+12x-2
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The only possible rational roots are of the form (plus or minus) p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. So in this polynomial the only possible rational roots are -2, -1, 1, and 2.

Simple quick substitution shows that none of those are roots.

It is a 4th degree polynomial, so there are 4 roots; and we now know they are all irrational. So they can only be determined approximately by numerical methods such as calculus or a graphing calculator.

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