Find a rational zero of the polynomial function and use it to find all the zeros of the function.
-$$f ( x ) = 2 x ^ { 4 } + 17 x ^ { 3 } + 58 x ^ { 2 } + 77 x + 26$$
A) $\left\{ - 2 , - \frac { 1 } { 2 } , - 3 + 2 i , - 3 - 2 i \right\}$
B) $\left\{ 2 , + \frac { 1 } { 2 } , - 2 + 3 i , - 2 - 3 i \right\}$
C) $\left\{ - 2 , + \frac { 1 } { 2 } , - 2 + 3 i , - 2 - 3 i \right\}$
D) $\left\{ 2 , - \frac { 1 } { 2 } , - 3 + 2 i , - 3 - 2 i \right\}$

Question

Quizplus · Accepted Answer

The rational zero theorem suggests testing factors of the constant term (26) over factors of the leading coefficient (2). Testing these, -2 is found to be a zero. Using synthetic division, the polynomial can be factored to find the remaining zeros, which include -1/2 and the complex conjugates -3 ± 2i.

Find a Rational Zero of the Polynomial Function and Use f(x)=2x4+17x3+58x2+77x+26f ( x ) = 2 x ^ { 4 } + 17 x ^ { 3 } + 58 x ^ { 2 } + 77 x + 26f(x)=2x4+17x3+58x2+77x+26

Find a Rational Zero of the Polynomial Function and Use $f ( x ) = 2 x ^ { 4 } + 17 x ^ { 3 } + 58 x ^ { 2 } + 77 x + 26$