Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
-$$f ( x ) = 6 x ^ { 3 } + 25 x ^ { 2 } + 12 x - 7$$
A) $- 1$ (rational), $- \frac { 7 } { 2 }$ (rational), $\frac { 1 } { 3 }$ (rational)
B) - 1 (rational), $\frac { 1 } { 3 }$ (rational), $\frac { 7 } { 2 }$ (rational)
C) $\frac { 1 } { 3 }$ (rational) (multiplicity 2 ); $- \frac { 7 } { 2 }$ (rational)
D) $- \frac { 1 } { 3 }$ (rational), $- \frac { 7 } { 2 }$ (rational), $\frac { 1 } { 3 }$ (rational)

Question

Quizplus · Accepted Answer

The zeros of the polynomial $f(x) = 6x^3 + 25x^2 + 12x - 7$ are $-1$, $-\frac{7}{2}$, and $\frac{1}{3}$, all of which are rational numbers.

Find All of the Real Zeros of the Function f(x)=6x3+25x2+12x−7f ( x ) = 6 x ^ { 3 } + 25 x ^ { 2 } + 12 x - 7f(x)=6x3+25x2+12x−7

Find All of the Real Zeros of the Function $f ( x ) = 6 x ^ { 3 } + 25 x ^ { 2 } + 12 x - 7$