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Find the zeros of the function. Enter the solutions from least to greatest. {:[f(x)=(x-5)(5x+2)],[" lesser "x=◻],[" greater "x=◻]:}

Find the zeros of the function. Enter the solutions from least to greatest.\newlinef(x)=(x−5)(5x+2) f(x)=(x-5)(5 x+2) \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.\newlinef(x)=(x−5)(5x+2) f(x)=(x-5)(5 x+2) \newlinelesser x= x= \newlinegreater x= x=
  1. Identify Zeros: Identify the zeros of the function by setting the function equal to zero.\newlineTo find the zeros of f(x)f(x), we set f(x)=0f(x) = 0 and solve for xx.\newline0=(x−5)(5x+2)0 = (x-5)(5x+2)
  2. Solve First Factor: Solve the first factor set to zero.\newlineSet the first factor equal to zero and solve for xx:\newlinex−5=0x - 5 = 0\newlinex=5x = 5
  3. Solve Second Factor: Solve the second factor set to zero.\newlineSet the second factor equal to zero and solve for xx:\newline5x+2=05x + 2 = 0\newline5x=−25x = -2\newlinex=−25x = -\frac{2}{5}
  4. Arrange Solutions: Arrange the solutions in ascending order.\newlineThe lesser xx is −25-\frac{2}{5}, and the greater xx is 55.

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