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Find the zeros of the function f(x)=2x^(2)+16.2 x+28. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=2x2+16.2x+28 f(x)=2 x^{2}+16.2 x+28 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Q. Find the zeros of the function f(x)=2x2+16.2x+28 f(x)=2 x^{2}+16.2 x+28 . 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 f(x)=2x2+16.2x+28f(x) = 2x^2 + 16.2x + 28 is a quadratic equation. To find the zeros of a quadratic equation, we can use 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: Apply the quadratic formula to find the zeros of the function.\newlineFor the given function, a=2a = 2, b=16.2b = 16.2, and c=28c = 28. Plugging these values into the quadratic formula gives us:\newlinex=−16.2±(16.2)2−4⋅2⋅282⋅2x = \frac{-16.2 \pm \sqrt{(16.2)^2 - 4 \cdot 2 \cdot 28}}{2 \cdot 2}
  3. Calculate Discriminant: Calculate the discriminant (the part under the square root in the quadratic formula).\newlineThe discriminant is b2−4acb^2 - 4ac, so we calculate:\newline(16.2)2−4×2×28=262.44−224=38.44(16.2)^2 - 4\times 2\times 28 = 262.44 - 224 = 38.44
  4. Calculate Square Root: Calculate the square root of the discriminant. 38.44≈6.20\sqrt{38.44} \approx 6.20
  5. Calculate Possible Values: Calculate the two possible values for xx using the quadratic formula.x=−16.2±6.204x = \frac{{-16.2 \pm 6.20}}{4}We have two solutions: one with the plus sign and one with the minus sign.
  6. Calculate First Zero: Calculate the first zero using the plus sign in the quadratic formula.\newlinex=−16.2+6.204x = \frac{{-16.2 + 6.20}}{4}\newlinex=−104x = \frac{{-10}}{4}\newlinex=−2.5x = -2.5
  7. Calculate Second Zero: Calculate the second zero using the minus sign in the quadratic formula.\newlinex=−16.2−6.204x = \frac{{-16.2 - 6.20}}{4}\newlinex=−22.44x = \frac{{-22.4}}{4}\newlinex=−5.6x = -5.6
  8. Round Zeros: Round the zeros to the nearest hundredth if necessary.\newlineThe zeros are already at the nearest hundredth, so we have:\newlinex≈−2.50x \approx -2.50 and x≈−5.60x \approx -5.60

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