Find the zeros of the function and state the multiplicities.
-$$f ( x ) = 2 x ^ { 5 } + 9 x ^ { 4 } + 7 x ^ { 3 }$$
A) $- 1$ (multiplicity $2.5 ) , - \frac { 7 } { 2 }$ (multiplicity $2.5$ )
B) 1 (multiplicity $2.5 ) , \frac { 7 } { 2 }$ (multiplicity $2.5$ )
C) 0 (multiplicity 3 ), 1 (multiplicity $1 ), \frac { 7 } { 2 }$ (multiplicity 1 )
D) 0 (multiplicity 3), $- 1$ (multiplicity $1 ), - \frac { 7 } { 2 }$ (multiplicity 1 )

Question

Quizplus · Accepted Answer

First, factor out the greatest common factor, which is $x^3$, giving $x^3(2x^2 + 9x + 7)$. The zeros are found by setting $x^3 = 0$ and $2x^2 + 9x + 7 = 0$. The first equation gives a zero at $x = 0$ with multiplicity 3. Solving the quadratic equation $2x^2 + 9x + 7 = 0$ using the quadratic formula or factoring (if possible) would give the other zeros, which are not $1$ or $\frac{7}{2}$ as in choices B and C, and multiplicities are always whole numbers, ruling out choice A.

Find the Zeros of the Function and State the Multiplicities f(x)=2x5+9x4+7x3f ( x ) = 2 x ^ { 5 } + 9 x ^ { 4 } + 7 x ^ { 3 }f(x)=2x5+9x4+7x3

Find the Zeros of the Function and State the Multiplicities $f ( x ) = 2 x ^ { 5 } + 9 x ^ { 4 } + 7 x ^ { 3 }$