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

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

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Full solution

Q. Find the zeros of the function. Enter the solutions from least to greatest.\newlinef(x)=(−x−2)(−2x−3)lesser x=□greater x=□\begin{array}{l} f(x)=(−x−2)(−2x−3) \text{lesser } x=\square \text{greater } x=\square \end{array}
  1. Factored function: Factored function: f(x)=(−x−2)(−2x−3)f(x) = (-x - 2)(-2x - 3)\newlineTo find the zeros of the function, we need to set the function equal to zero and solve for xx.\newline(−x−2)(−2x−3)=0(-x - 2)(-2x - 3) = 0
  2. Setting the first factor equal to zero: First, let's find the zero by setting the first factor equal to zero.\newline−x−2=0-x - 2 = 0\newlineNow, solve for x.\newline−x=2-x = 2\newlinex=−2x = -2
  3. Solving for x: Next, find the zero by setting the second factor equal to zero.\newline−2x−3=0-2x - 3 = 0\newlineNow, solve for x.\newline−2x=3-2x = 3\newlinex = −32-\frac{3}{2} or x = −1.5-1.5
  4. Setting the second factor equal to zero: We have found two zeros: x=−2x = -2 and x=−1.5x = -1.5.\newlineTo list them in ascending order:\newlinex=−1.5x = -1.5 (lesser)\newlinex=−2x = -2 (greater)

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