For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
-$f ( x ) = 3 \left( x ^ { 2 } + 5 \right) ( x + 6 ) ^ { 2 }$
A) -6, multiplicity 2, touches x-axis
B) -5, multiplicity 1, touches x-axis; -6, multiplicity 2, crosses x-axis
C) -6, multiplicity 2, crosses x-axis
D) -5, multiplicity 1, crosses x-axis; -6, multiplicity 2, touches x-axis

Question

Quizplus · Accepted Answer

The polynomial $f(x) = 3(x^2 + 5)(x + 6)^2$ has one real zero at $x = -6$ with multiplicity 2. Since the multiplicity is even, the graph touches the x-axis at this intercept. There are no real zeros at $x = -5$, as that would imply $x^2 + 5 = 0$, which does not have real solutions.

For the Polynomial, List Each Real Zero and Its Multiplicity f(x)=3(x2+5)(x+6)2f ( x ) = 3 \left( x ^ { 2 } + 5 \right) ( x + 6 ) ^ { 2 }f(x)=3(x2+5)(x+6)2

For the Polynomial, List Each Real Zero and Its Multiplicity $f ( x ) = 3 \left( x ^ { 2 } + 5 \right) ( x + 6 ) ^ { 2 }$