Find the zeros of the function and state the multiplicities.
-$$f ( x ) = - 2 x ^ { 6 } ( x + 7 ) ^ { 2 } ( x - 5 ) ^ { 6 }$$
A) $- 7$ (multiplicity 2), 5 (multiplicity 6)
B) 7 (multiplicity 2), $- 5$ (multiplicity 6)
C) 0 (multiplicity 6), 7 (multiplicity 2), $- 5$ (multiplicity 6)
D) 0 (multiplicity 6), $- 7$ (multiplicity 2), 5 (multiplicity 6)

Question

Quizplus · Accepted Answer

The zeros of the function are found by setting each factor equal to zero. The factor $x^6$ has a zero at $x = 0$ with multiplicity 6, the factor $(x + 7)^2$ has a zero at $x = -7$ with multiplicity 2, and the factor $(x - 5)^6$ has a zero at $x = 5$ with multiplicity 6.

Find the Zeros of the Function and State the Multiplicities f(x)=−2x6(x+7)2(x−5)6f ( x ) = - 2 x ^ { 6 } ( x + 7 ) ^ { 2 } ( x - 5 ) ^ { 6 }f(x)=−2x6(x+7)2(x−5)6

Find the Zeros of the Function and State the Multiplicities $f ( x ) = - 2 x ^ { 6 } ( x + 7 ) ^ { 2 } ( x - 5 ) ^ { 6 }$