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Find the zeros of the function f(x)=2x^(2)-20.9 x+52.6. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=2x2−20.9x+52.6 f(x)=2 x^{2}-20.9 x+52.6 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Q. Find the zeros of the function f(x)=2x2−20.9x+52.6 f(x)=2 x^{2}-20.9 x+52.6 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Identify Equation Type and Method: Identify the type of equation and the method to find its zeros.\newlineWe have a quadratic equation of the form f(x)=ax2+bx+cf(x) = ax^2 + bx + c, where a=2a = 2, b=−20.9b = -20.9, and c=52.6c = 52.6. 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 find the zeros.\newlineFirst, calculate the discriminant b2−4acb^2 - 4ac.\newlineDiscriminant = (−20.9)2−4×2×52.6(-20.9)^2 - 4 \times 2 \times 52.6\newlineDiscriminant = 436.81−420.8436.81 - 420.8\newlineDiscriminant = 16.0116.01
  3. Calculate Discriminant: Since the discriminant is positive, there are two real and distinct solutions. Now, calculate the zeros using the quadratic formula.\newlinex=−(−20.9)±16.01(2⋅2)x = \frac{-(-20.9) \pm \sqrt{16.01}}{(2 \cdot 2)}\newlinex=20.9±44x = \frac{20.9 \pm 4}{4}
  4. Calculate Zeros: Calculate the two zeros.\newlineFirst zero:\newlinex1=20.9+44x_1 = \frac{20.9 + 4}{4}\newlinex1=24.94x_1 = \frac{24.9}{4}\newlinex1=6.225x_1 = 6.225\newlineRounded to the nearest hundredth, x1≈6.23x_1 \approx 6.23\newlineSecond zero:\newlinex2=20.9−44x_2 = \frac{20.9 - 4}{4}\newlinex2=16.94x_2 = \frac{16.9}{4}\newlinex2=4.225x_2 = 4.225\newlineRounded to the nearest hundredth, x2≈4.23x_2 \approx 4.23

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