Find the zero(s) of \( f(x)=8.53 x^{2}-9.81 x-5.69 \) to three decimal places. If there is more than one zero, write all them on the same line, separated by commas.

To find the zeros of the quadratic function \( f(x) = 8.53 x^{2} - 9.81 x - 5.69 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 8.53 \), \( b = -9.81 \), and \( c = -5.69 \). First, calculate the discriminant: \[ b^2 - 4ac = (-9.81)^2 - 4 \cdot 8.53 \cdot (-5.69) = 96.4561 + 193.5244 = 289.9805 \] Now, applying the quadratic formula: \[ x = \frac{-(-9.81) \pm \sqrt{289.9805}}{2 \cdot 8.53} = \frac{9.81 \pm 17.038}{17.06} \] Calculating the two possible values for \( x \): 1. \( x_1 = \frac{9.81 + 17.038}{17.06} \approx \frac{26.848}{17.06} \approx 1.576 \) 2. \( x_2 = \frac{9.81 - 17.038}{17.06} \approx \frac{-7.228}{17.06} \approx -0.424 \) Thus, the zeros of the function, rounded to three decimal places, are: \[ \boxed{1.576, -0.424} \]