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Find the zeros of the function f(x)=x^(2)+9.4 x+19.8. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=x2+9.4x+19.8 f(x)=x^{2}+9.4 x+19.8 . 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+9.4x+19.8 f(x)=x^{2}+9.4 x+19.8 . 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 f(x)=ax2+bx+cf(x) = ax^2 + bx + c. To find the zeros of the function, we can use the quadratic formula, which is 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)=x2+9.4x+19.8f(x) = x^2 + 9.4x + 19.8, we have a=1a = 1, b=9.4b = 9.4, and c=19.8c = 19.8. Plugging these values into the quadratic formula gives us:\newlinex=−9.4±9.42−4⋅1⋅19.82⋅1x = \frac{-9.4 \pm \sqrt{9.4^2 - 4 \cdot 1 \cdot 19.8}}{2 \cdot 1}
  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:\newlineDiscriminant = 9.42−4×1×19.8=88.36−79.2=9.169.4^2 - 4\times1\times19.8 = 88.36 - 79.2 = 9.16
  4. Find Solutions Using Formula: Since the discriminant is positive, we have two real and distinct solutions. Calculate the two solutions using the quadratic formula.\newlinex=−9.4±9.162x = \frac{-9.4 \pm \sqrt{9.16}}{2}\newlineFirst, we find the square root of the discriminant:\newline9.16≈3.03\sqrt{9.16} \approx 3.03
  5. Calculate Zeros: Calculate the two zeros of the function.\newlinex1=−9.4+3.032≈−6.372≈−3.185x_1 = \frac{-9.4 + 3.03}{2} \approx \frac{-6.37}{2} \approx -3.185\newlinex2=−9.4−3.032≈−12.432≈−6.215x_2 = \frac{-9.4 - 3.03}{2} \approx \frac{-12.43}{2} \approx -6.215\newlineRound both values to the nearest hundredth:\newlinex1≈−3.19x_1 \approx -3.19\newlinex2≈−6.22x_2 \approx -6.22

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