Find the zeros of the function \( f(x)=-0.9 x^{2}-2.3 x+1 \). Round val thousandths (if necessary).

To find the zeros of the function \( f(x) = -0.9x^2 - 2.3x + 1 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = -0.9 \), \( b = -2.3 \), and \( c = 1 \). First, we calculate the discriminant \( b^2 - 4ac \): \[ b^2 = (-2.3)^2 = 5.29 \] \[ 4ac = 4 \cdot (-0.9) \cdot 1 = -3.6 \] \[ b^2 - 4ac = 5.29 - (-3.6) = 5.29 + 3.6 = 8.89 \] Now we can substitute \( a \), \( b \), and the discriminant into the quadratic formula: \[ x = \frac{-(-2.3) \pm \sqrt{8.89}}{2 \cdot (-0.9)} \] \[ x = \frac{2.3 \pm \sqrt{8.89}}{-1.8} \] Next, we calculate \( \sqrt{8.89} \): \[ \sqrt{8.89} \approx 2.983 \] Now we can find the two possible values for \( x \): 1. For the positive root: \[ x_1 = \frac{2.3 + 2.983}{-1.8} = \frac{5.283}{-1.8} \approx -2.935 \] 2. For the negative root: \[ x_2 = \frac{2.3 - 2.983}{-1.8} = \frac{-0.683}{-1.8} \approx 0.379 \] Thus, the zeros of the function \( f(x) = -0.9x^2 - 2.3x + 1 \) are approximately: \[ x_1 \approx -2.935 \quad \text{and} \quad x_2 \approx 0.379 \] Rounding to the nearest thousandths, the zeros are: \[ \boxed{-2.935} \quad \text{and} \quad \boxed{0.379} \]