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Find the zeros of the function f(x)=2x^(2)-22 x+56. Round values to the nearest hundredth (if necessary). Answer: x=

Find the zeros of the function f(x)=2x2−22x+56 f(x)=2 x^{2}-22 x+56 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=

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Q. Find the zeros of the function f(x)=2x2−22x+56 f(x)=2 x^{2}-22 x+56 . Round values to the nearest hundredth (if necessary).\newlineAnswer: x= x=
  1. Set Quadratic Function Equal: Set the quadratic function equal to zero to find its zeros.\newlinef(x)=2x2−22x+56=0f(x) = 2x^2 - 22x + 56 = 0
  2. Factor Quadratic Equation: Factor the quadratic equation, if possible, to find the values of xx that make the function equal to zero.\newlineThe quadratic factors as (2x−8)(x−7)=0(2x - 8)(x - 7) = 0
  3. Solve for x: Set each factor equal to zero and solve for x.\newline2x−8=02x - 8 = 0 or x−7=0x - 7 = 0
  4. Solve 2x−8=02x - 8 = 0: Solve the first equation 2x−8=02x - 8 = 0 for xx.\newline2x=82x = 8\newlinex=82x = \frac{8}{2}\newlinex=4x = 4
  5. Solve x−7=0x - 7 = 0: Solve the second equation x−7=0x - 7 = 0 for xx.x=7x = 7
  6. Check Solutions: Check the solutions by substituting them back into the original equation to ensure they make the equation true.\newlineFor x=4x = 4: f(4)=2(4)2−22(4)+56=32−88+56=0f(4) = 2(4)^2 - 22(4) + 56 = 32 - 88 + 56 = 0\newlineFor x=7x = 7: f(7)=2(7)2−22(7)+56=98−154+56=0f(7) = 2(7)^2 - 22(7) + 56 = 98 - 154 + 56 = 0\newlineBoth solutions make the equation true.

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