Find the zeros of the function.
-$$f ( x ) = x ^ { 3 } - 17 x ^ { 2 } + 94 x - 168$$
A) 7,6 , and 4
B) $- 7 , - 6$, and $- 4$
C) 1,6 , and 4
D) 0,7 , and 4

Question

Quizplus · Accepted Answer

The zeros of the function can be found by factoring the cubic polynomial or using synthetic division. Factoring $f(x) = x^3 - 17x^2 + 94x - 168$, we can try to find a root by trial and error or by using the Rational Root Theorem. Checking for easy roots, we find that $x = 7$ is a root because $f(7) = 0$. Using synthetic division or polynomial long division with $x - 7$, we can factor the polynomial as $(x - 7)(x^2 - 10x + 24)$. Further factoring the quadratic part gives $(x - 7)(x - 4)(x - 6)$, indicating the zeros are 7, 4, and 6.

Find the Zeros of the Function f(x)=x3−17x2+94x−168f ( x ) = x ^ { 3 } - 17 x ^ { 2 } + 94 x - 168f(x)=x3−17x2+94x−168

Find the Zeros of the Function $f ( x ) = x ^ { 3 } - 17 x ^ { 2 } + 94 x - 168$