Find the zeros of the function and state the multiplicities.

If there is more than one answer, separate them with commas. Select “None” if applicable
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Part 1 of 2
The zero(s) of

Ask by Donnelly Stuart. in the United States

Mar 20,2025

Question

Find the zeros of the function and state the multiplicities.

If there is more than one answer, separate them with commas. Select “None” if applicable
Part: 0 / 2
Part 1 of 2
The zero(s) of

Ask by Donnelly Stuart. in the United States

Mar 20,2025

UpStudy AI · Accepted Answer

The function is given by

$$
f(x) = [x - (4-\sqrt{3})][x - (4+\sqrt{3})].
$$

To find the zeros, we set $$ f(x) = 0 $$ and solve:

$$
[x - (4-\sqrt{3})][x - (4+\sqrt{3})] = 0.
$$

Using the Zero Product Property, we have:

$$
x - (4-\sqrt{3}) = 0 \quad \text{or} \quad x - (4+\sqrt{3}) = 0.
$$

Solving each equation gives:

$$
x = 4-\sqrt{3} \quad \text{or} \quad x = 4+\sqrt{3}.
$$

Each zero appears only once in the factorization, so both have a multiplicity of 1.

Thus, the zeros of $$ f $$ are:

$$
4-\sqrt{3},\ 4+\sqrt{3}.
$$
The zeros of $$ f $$ are $$ 4-\sqrt{3} $$ and $$ 4+\sqrt{3} $$.