Find the zeros of the function and state the multiplicities.
-$$f ( x ) = 4 x ( 9 x + 8 ) ( 2 x + 5 ) ( x + \sqrt { 6 } ) ( x - \sqrt { 6 } )$$
A) $0 , \frac { 8 } { 9 } , \frac { 5 } { 2 } , \pm 6$; each of multiplicity 1
B) $0 , - \frac { 8 } { 9 } , - \frac { 5 } { 2 } ;$ each of multiplicity 1 ; and $\sqrt { 6 }$ of multiplicity 2
C) $0 , - \frac { 8 } { 9 } , - \frac { 5 } { 2 } , \pm \sqrt { 6 }$; each of multiplicity 1
D) $0 , \frac { 8 } { 9 } , \frac { 5 } { 2 }$; each of multiplicity 1 ; and 6 of multiplicity 2

Question

Quizplus · Accepted Answer

The zeros of the function are found by setting each factor equal to zero: $4x = 0$ gives $x = 0$, $9x + 8 = 0$ gives $x = -\frac{8}{9}$, $2x + 5 = 0$ gives $x = -\frac{5}{2}$, and $x + \sqrt{6} = 0$ and $x - \sqrt{6} = 0$ give $x = -\sqrt{6}$ and $x = \sqrt{6}$ respectively. Each factor appears only once, so each zero has a multiplicity of 1.

Find the Zeros of the Function and State the Multiplicities f(x)=4x(9x+8)(2x+5)(x+6)(x−6)f ( x ) = 4 x ( 9 x + 8 ) ( 2 x + 5 ) ( x + \sqrt { 6 } ) ( x - \sqrt { 6 } )f(x)=4x(9x+8)(2x+5)(x+6​)(x−6​)

Find the Zeros of the Function and State the Multiplicities $f ( x ) = 4 x ( 9 x + 8 ) ( 2 x + 5 ) ( x + \sqrt { 6 } ) ( x - \sqrt { 6 } )$