Assignment Overview $$ 1 \approx $$ DeltaMath Score: 0/5 Penalty: 1 off Finding Zeros with Technology Question Video Examples Find the zeros of the function $$ f(x)=x^{2}-7.2 x+10 $$. Round values to the nearest thousandths (if necessary). Answer Attempt 1 out of 2 † Add a Zero No Zeros $$ x= $$ $$ \square $$ Submit Answer

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UpStudy AI · Accepted Answer

To find the zeros of the function $$ f(x) = x^{2} - 7.2x + 10 $$, we'll solve the equation $$ f(x) = 0 $$. This means finding the values of $$ x $$ where the function crosses the x-axis.

### Step 1: Set the Function Equal to Zero
$$
x^{2} - 7.2x + 10 = 0
$$

### Step 2: Use the Quadratic Formula
For a quadratic equation of the form $$ ax^{2} + bx + c = 0 $$, the solutions (zeros) can be found using the quadratic formula:
$$
x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}
$$
Here, $$ a = 1 $$, $$ b = -7.2 $$, and $$ c = 10 $$.

### Step 3: Calculate the Discriminant
$$
\Delta = b^{2} - 4ac = (-7.2)^{2} - 4(1)(10) = 51.84 - 40 = 11.84
$$

### Step 4: Compute the Square Root of the Discriminant
$$
\sqrt{11.84} \approx 3.44
$$

### Step 5: Find the Two Zeros
$$
x = \frac{7.2 \pm 3.44}{2}
$$

1. **First Zero ($$ x_1 $$)**
$$
x_1 = \frac{7.2 + 3.44}{2} = \frac{10.64}{2} = 5.32
$$

2. **Second Zero ($$ x_2 $$)**
$$
x_2 = \frac{7.2 - 3.44}{2} = \frac{3.76}{2} = 1.88
$$

### Step 6: Round to the Nearest Thousandth
Both zeros are already precise to two decimal places. However, to express them to the nearest thousandth:

$$
x_1 = 5.320 \
x_2 = 1.880
$$

### Final Answer
$$
x = 1.880 \quad \text{and} \quad x = 5.320
$$
The zeros of the function $$ f(x) = x^{2} - 7.2x + 10 $$ are $$ x = 1.880 $$ and $$ x = 5.320 $$.

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