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Find the zeros of the function. Enter the solutions from least to greatest. h(x)=(−4x−5)(−x+5) h(x)=(-4x -5)(-x +5)

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Determine end behavior of polynomial and rational functionsright chevron icon

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Q. Find the zeros of the function. Enter the solutions from least to greatest. h(x)=(−4x−5)(−x+5) h(x)=(-4x -5)(-x +5)
  1. Identify Zeros: Identify the zeros of the function by setting each factor equal to zero.\newlineFor the first factor, we have −4x−5=0-4x - 5 = 0.\newlineTo solve for x, we add 55 to both sides of the equation.\newline−4x−5+5=0+5-4x - 5 + 5 = 0 + 5\newline−4x=5-4x = 5\newlineNow, we divide both sides by −4-4 to isolate xx.\newline−4x/−4=5/−4-4x / -4 = 5 / -4\newlinex=−5/4x = -5 / 4
  2. Solve First Factor: Solve for the zero from the second factor, which is −x+5=0-x + 5 = 0. To solve for xx, we subtract 55 from both sides of the equation. −x+5−5=0−5-x + 5 - 5 = 0 - 5 −x=−5-x = -5 Now, we multiply both sides by −1-1 to isolate xx. −x×−1=−5×−1-x \times -1 = -5 \times -1 x=5x = 5
  3. Solve Second Factor: Arrange the solutions from least to greatest.\newlineThe solutions we found are x=−54x = -\frac{5}{4} and x=5x = 5.\newlineSince -\frac{5}{4} < 5, the solutions in order from least to greatest are:\newlinex=−54,x=5x = -\frac{5}{4}, x = 5

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