Finding Zeros with Technology Question © Video Examples Find the zeros of the function \( f(x)=0.3 x^{2}-3 x+5.5 \). Round values to the nearest thousandths (if necessary). Answer Attempt 1 out of 2 \( \oplus \) Add a Zero \( \Theta \) No Zeros \( x=\square \) Submit Answer

To find the zeros of the function \( f(x) = 0.3x^2 - 3x + 5.5 \), we'll solve the equation: \[ 0.3x^2 - 3x + 5.5 = 0 \] ### Step 1: Identify the Coefficients - \( a = 0.3 \) - \( b = -3 \) - \( c = 5.5 \) ### Step 2: Calculate the Discriminant The discriminant \( D \) is given by: \[ D = b^2 - 4ac \] \[ D = (-3)^2 - 4(0.3)(5.5) = 9 - 6.6 = 2.4 \] Since \( D > 0 \), there are **two real zeros**. ### Step 3: Use the Quadratic Formula The quadratic formula to find the zeros is: \[ x = \frac{-b \pm \sqrt{D}}{2a} \] Plugging in the values: \[ x = \frac{3 \pm \sqrt{2.4}}{0.6} \] ### Step 4: Calculate the Zeros 1. **First Zero (\( x_1 \)):** \[ x_1 = \frac{3 + \sqrt{2.4}}{0.6} \approx \frac{3 + 1.549}{0.6} = \frac{4.549}{0.6} \approx 7.582 \] 2. **Second Zero (\( x_2 \)):** \[ x_2 = \frac{3 - \sqrt{2.4}}{0.6} \approx \frac{3 - 1.549}{0.6} = \frac{1.451}{0.6} \approx 2.418 \] ### Step 5: Round to the Nearest Thousandths - \( x_1 \approx 7.582 \) - \( x_2 \approx 2.418 \) ### **Final Answer:** The zeros of the function are: \[ x \approx 2.418 \quad \text{and} \quad x \approx 7.582 \]