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Find the zeros of the function f(x)=2x^(2)-8.4 x+5.2. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=2x2−8.4x+5.2 f(x)=2 x^{2}-8.4 x+5.2 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Q. Find the zeros of the function f(x)=2x2−8.4x+5.2 f(x)=2 x^{2}-8.4 x+5.2 . 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)=2x2−8.4x+5.2f(x) = 2x^2 - 8.4x + 5.2 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 equation ax2+bx+c=0ax^2 + bx + c = 0.
  2. Apply Quadratic Formula: Apply the quadratic formula to the given equation.\newlineFor the equation f(x)=2x2−8.4x+5.2f(x) = 2x^2 - 8.4x + 5.2, the coefficients are a=2a = 2, b=−8.4b = -8.4, and c=5.2c = 5.2. Plugging these values into the quadratic formula gives us:\newlinex=−(−8.4)±(−8.4)2−4⋅2⋅5.22⋅2x = \frac{-(-8.4) \pm \sqrt{(-8.4)^2 - 4 \cdot 2 \cdot 5.2}}{2 \cdot 2}\newlinex=8.4±70.56−41.64x = \frac{8.4 \pm \sqrt{70.56 - 41.6}}{4}\newlinex=8.4±28.964x = \frac{8.4 \pm \sqrt{28.96}}{4}
  3. Simplify Expression and Calculate: Simplify the expression under the square root and calculate the zeros.\newlinex=8.4±28.964x = \frac{8.4 \pm \sqrt{28.96}}{4}\newlinex=8.4±5.384x = \frac{8.4 \pm 5.38}{4}\newlineNow we have two possible solutions for xx:\newlinex1=8.4+5.384x_1 = \frac{8.4 + 5.38}{4}\newlinex2=8.4−5.384x_2 = \frac{8.4 - 5.38}{4}
  4. Calculate First Zero: Calculate the first zero x1x_1.x1=8.4+5.384x_1 = \frac{8.4 + 5.38}{4}x1=13.784x_1 = \frac{13.78}{4}x1=3.445x_1 = 3.445Rounded to the nearest hundredth, x1≈3.45x_1 \approx 3.45
  5. Calculate Second Zero: Calculate the second zero (x2x_2).\newlinex2=(8.4−5.38)/4x_2 = (8.4 - 5.38) / 4\newlinex2=3.02/4x_2 = 3.02 / 4\newlinex2=0.755x_2 = 0.755\newlineRounded to the nearest hundredth, x2≈0.76x_2 \approx 0.76

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