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Find the zeros of the function f(x)=-1.8x^(2)-8.3 x-4.5. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=−1.8x2−8.3x−4.5 f(x)=-1.8 x^{2}-8.3 x-4.5 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Q. Find the zeros of the function f(x)=−1.8x2−8.3x−4.5 f(x)=-1.8 x^{2}-8.3 x-4.5 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Identify Equation Type: Identify the type of equation and the method to find its zeros.\newlineThe given function is a quadratic equation of the form ax2+bx+c=0ax^2 + bx + c = 0. To find the zeros of the function, we can use the quadratic formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  2. Apply Quadratic Formula: Apply the quadratic formula to the given function.\newlineFor the function f(x)=−1.8x2−8.3x−4.5f(x) = -1.8x^2 - 8.3x - 4.5, the coefficients are a=−1.8a = -1.8, b=−8.3b = -8.3, and c=−4.5c = -4.5. Plugging these values into the quadratic formula gives us:\newlinex=−(−8.3)±(−8.3)2−4(−1.8)(−4.5)2(−1.8)x = \frac{-(-8.3) \pm \sqrt{(-8.3)^2 - 4(-1.8)(-4.5)}}{2(-1.8)}
  3. Simplify Discriminant: Simplify the expression under the square root (the discriminant). The discriminant is (−8.3)2−4(−1.8)(−4.5)=68.89−4(8.1)=68.89−32.4=36.49(-8.3)^2 - 4(-1.8)(-4.5) = 68.89 - 4(8.1) = 68.89 - 32.4 = 36.49.
  4. Calculate Square Root: Calculate the square root of the discriminant. 36.49=6.04\sqrt{36.49} = 6.04.
  5. Continue Quadratic Formula: Continue with the quadratic formula using the simplified discriminant. x=8.3±6.04−3.6x = \frac{8.3 \pm 6.04}{-3.6}
  6. Solve for Zeros: Solve for the two possible values of xx.\newlineFirst zero:\newlinex=8.3+6.04−3.6=14.34−3.6≈−3.98x = \frac{8.3 + 6.04}{-3.6} = \frac{14.34}{-3.6} \approx -3.98\newlineSecond zero:\newlinex=8.3−6.04−3.6=2.26−3.6≈−0.63x = \frac{8.3 - 6.04}{-3.6} = \frac{2.26}{-3.6} \approx -0.63
  7. Round Zeros: Round the zeros to the nearest hundredth.\newlineFirst zero: x≈−3.98x \approx -3.98 (already rounded to the nearest hundredth)\newlineSecond zero: x≈−0.63x \approx -0.63 (already rounded to the nearest hundredth)

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