For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
-$$f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }$$
A) No real zeros

B) $- 1$, multiplicity 1 , touches $x$-axis; $- 6$, multiplicity 2 , crosses $x$-axis

C) 1 , multiplicity 1 , crosses $x$-axis; $- 1$, multiplicity 1 , crosses $x$-axis;
$\sqrt { 6 }$, multiplicity 2 , touches $x$-axis; $- \sqrt { 6 }$, multiplicity 2 , touches $x$-axis

D) $- 1$, multiplicity 1 , crosses $x$-axis; $- 6$, multiplicity 2 , touches $x$-axis

Question

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
-$$f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }$$
A) No real zeros

B) $- 1$, multiplicity 1 , touches $x$-axis; $- 6$, multiplicity 2 , crosses $x$-axis

C) 1 , multiplicity 1 , crosses $x$-axis; $- 1$, multiplicity 1 , crosses $x$-axis; 
$\sqrt { 6 }$, multiplicity 2 , touches $x$-axis; $- \sqrt { 6 }$, multiplicity 2 , touches $x$-axis

D) $- 1$, multiplicity 1 , crosses $x$-axis; $- 6$, multiplicity 2 , touches $x$-axis

Quizplus · Accepted Answer

The given polynomial $f(x) = 2(x^2 + 1)(x^2 + 6)^2$ does not have any real zeros because both $x^2 + 1$ and $x^2 + 6$ are always positive for all real numbers $x$.

For the Polynomial, List Each Real Zero and Its Multiplicity f(x)=2(x2+1)(x2+6)2f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }f(x)=2(x2+1)(x2+6)2

For the Polynomial, List Each Real Zero and Its Multiplicity $f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }$