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

Find the zeros of the function. Enter the solutions from least to greatest.\newlineg(x)=(x−2)(3x+3) g(x) = (x - 2)(3x + 3) , 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.\newlineg(x)=(x−2)(3x+3) g(x) = (x - 2)(3x + 3) , lesser x=□ \text{lesser } x = \square , greater x=□ \text{greater } x = \square
  1. Factored function: Factored function: g(x)=(x−2)(3x+3)g(x) = (x - 2)(3x + 3)\newlineTo find the zeros of the function, we set g(x)g(x) equal to zero.\newline(x−2)(3x+3)=0(x - 2)(3x + 3) = 0
  2. First zero: First zero: x−2=0x - 2 = 0\newlineSolve for xx:\newlinex−2+2=0+2x - 2 + 2 = 0 + 2\newlinex=2x = 2
  3. Second zero: Second zero: 3x+3=03x + 3 = 0
    Solve for xx:
    3x+3−3=0−33x + 3 - 3 = 0 - 3
    3x=−33x = -3
    Divide both sides by 33:
    x=−33x = \frac{-3}{3}
    x=−1x = -1
  4. Roots of the function: We have found the two zeros of the function:\newlinex=2x = 2\newlinex=−1x = -1\newlineList the solutions from least to greatest.\newlineRoots of the function: −1-1, 22

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