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Find the zeros of the function. Enter the solutions from least to greatest. {:[h(x)=(-4x-3)(x-3)],[" lesser "x=◻],[" greater "x=◻]:}

Find the zeros of the function. Enter the solutions from least to greatest.\newlineh(x)=(−4x−3)(x−3) h(x)=(-4 x-3)(x-3) \newlinelesser x= x= \newlinegreater x= x=

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Full solution

Q. Find the zeros of the function. Enter the solutions from least to greatest.\newlineh(x)=(−4x−3)(x−3) h(x)=(-4 x-3)(x-3) \newlinelesser x= x= \newlinegreater x= x=
  1. Set Function Equal to Zero: To find the zeros of the function h(x)h(x), we need to set the function equal to zero and solve for xx.h(x)=0h(x) = 0 when (−4x−3)(x−3)=0(-4x - 3)(x - 3) = 0.We can find the zeros by setting each factor equal to zero and solving for xx.
  2. Find Zeros of First Factor: First, let's set the first factor equal to zero and solve for xx.−4x−3=0-4x - 3 = 0Add 33 to both sides to isolate the term with xx.−4x=3-4x = 3Now, divide both sides by −4-4 to solve for xx.x=3−4x = \frac{3}{-4}x=−34x = -\frac{3}{4}This is our first zero.
  3. Find Zeros of Second Factor: Next, let's set the second factor equal to zero and solve for xx.x−3=0x - 3 = 0Add 33 to both sides to solve for xx.x=3x = 3This is our second zero.
  4. Enter Solutions in Order: Now we have both zeros of the function h(x)h(x): −34-\frac{3}{4} and 33. We need to enter the solutions from least to greatest. The lesser xx is −34-\frac{3}{4}, and the greater xx is 33.

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