QuestionPoints: 0 of 1
Find the zeros of the polynomial function and state the multiplicity of each. $$f(x)=x^{4}-11 x^{2}+18$$
The smallest zero is $\square$ with multiplicity $\square$ 1. . (Type an exact answer, using radicals as needed.) The smaller middle zero is $\square$ with multiplicity $\square$ $\square$.

Studdy Solution
Determine the multiplicity of each zero. Since the original polynomial was quadratic in form with respect to $y$, each solution for $y$ corresponds to two solutions for $x$.
The zeros are: - $x = -3$ with multiplicity 1 - $x = 3$ with multiplicity 1 - $x = -\sqrt{2}$ with multiplicity 1 - $x = \sqrt{2}$ with multiplicity 1
The smallest zero is $-3$ with multiplicity 1. The smaller middle zero is $-\sqrt{2}$ with multiplicity 1.