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Find the zeros of the function. Enter the solutions from least to greatest. {:[f(x)=(x-3)(2x-8)],[" lesser "x=◻],[" greater "x=◻]:}

Find the zeros of the function. Enter the solutions from least to greatest.\newlinef(x)=(x−3)(2x−8) f(x) = (x - 3)(2x - 8) , lesser x=□ \text{lesser } x = \square , greater x=□ \text{greater } x = \square

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Full solution

Q. Find the zeros of the function. Enter the solutions from least to greatest.\newlinef(x)=(x−3)(2x−8) f(x) = (x - 3)(2x - 8) , lesser x=□ \text{lesser } x = \square , greater x=□ \text{greater } x = \square
  1. Factored function: Factored function: f(x)=(x−3)(2x−8)f(x) = (x - 3)(2x - 8)\newlineTo find the zeros of the function, we need to set the function equal to zero and solve for xx.\newline0=(x−3)(2x−8)0 = (x - 3)(2x - 8)
  2. First zero: First zero: Solve x−3=0x - 3 = 0\newlineAdd 33 to both sides of the equation.\newlinex−3+3=0+3x - 3 + 3 = 0 + 3\newlinex=3x = 3
  3. Second zero: Second zero: Solve 2x−8=02x - 8 = 0
    Add 88 to both sides of the equation.
    2x−8+8=0+82x - 8 + 8 = 0 + 8
    2x=82x = 8
    Divide both sides by 22.
    2x2=82\frac{2x}{2} = \frac{8}{2}
    x=4x = 4
  4. Zeros of the function: We have found the two zeros of the function:\newlinex = 33\newlinex = 44\newlineSince 33 is less than 44, we have the solutions in ascending order.

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