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Find the zeros of the function f(x)=-x^(2)-8.7 x-16. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=−x2−8.7x−16 f(x)=-x^{2}-8.7 x-16 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Q. Find the zeros of the function f(x)=−x2−8.7x−16 f(x)=-x^{2}-8.7 x-16 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Identify Quadratic Equation: To find the zeros of the function f(x)=−x2−8.7x−16f(x) = -x^2 - 8.7x - 16, we need to solve the equation −x2−8.7x−16=0-x^2 - 8.7x - 16 = 0. This is a quadratic equation, which can be solved by using the quadratic formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the terms x2x^2, xx, and the constant term, respectively.
  2. Apply Quadratic Formula: In our equation, a=−1a = -1, b=−8.7b = -8.7, and c=−16c = -16. Plugging these values into the quadratic formula, we get:\newlinex=−(−8.7)±(−8.7)2−4(−1)(−16)2(−1)x = \frac{-(-8.7) \pm \sqrt{(-8.7)^2 - 4(-1)(-16)}}{2(-1)}
  3. Simplify Equation: Simplify the equation: x=8.7±75.69−64−2x = \frac{8.7 \pm \sqrt{75.69 - 64}}{-2}
  4. Calculate Square Root: Continue simplifying: x=8.7±11.69−2x = \frac{8.7 \pm \sqrt{11.69}}{-2}
  5. Find Two Solutions: Calculate the square root of 11.6911.69 to two decimal places: 11.69≈3.42\sqrt{11.69} \approx 3.42
  6. Calculate First Solution: Now we have two possible solutions for xx:x=8.7+3.42−2x = \frac{8.7 + 3.42}{-2} or x=8.7−3.42−2x = \frac{8.7 - 3.42}{-2}
  7. Calculate Second Solution: Calculate the first solution:\newlinex=(8.7+3.42)/−2x = (8.7 + 3.42) / -2\newlinex=12.12/−2x = 12.12 / -2\newlinex≈−6.06x \approx -6.06
  8. Calculate Second Solution: Calculate the first solution:\newlinex=8.7+3.42−2x = \frac{8.7 + 3.42}{-2}\newlinex=12.12−2x = \frac{12.12}{-2}\newlinex≈−6.06x \approx -6.06Calculate the second solution:\newlinex=8.7−3.42−2x = \frac{8.7 - 3.42}{-2}\newlinex=5.28−2x = \frac{5.28}{-2}\newlinex≈−2.64x \approx -2.64

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