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Find the zeros of the function. Enter the solutions from least to greatest.\newlinef(x)=(x−5)(5x+2)f(x)=(x-5)(5x+2)\newlinelesser x=□x=\square\newlinegreater x=□x=\square

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Q. Find the zeros of the function. Enter the solutions from least to greatest.\newlinef(x)=(x−5)(5x+2)f(x)=(x-5)(5x+2)\newlinelesser x=□x=\square\newlinegreater x=□x=\square
  1. Set Function Equal to Zero: To find the zeros of the function, we need to set the function equal to zero and solve for xx. This means we need to find the values of xx that make the product (x−5)(5x+2)(x-5)(5x+2) equal to zero.
  2. Apply Zero Product Property: According to the zero product property, if the product of two factors is 00, then at least one of the factors must be 00. Therefore, we can set each factor equal to 00 and solve for xx.
  3. Solve for x: First, we set the first factor equal to zero: (x−5)=0(x - 5) = 0. Solving for x gives us x=5x = 5.
  4. Find First Solution: Next, we set the second factor equal to zero: (5x+2)=0(5x + 2) = 0. Solving for xx gives us x=−25x = -\frac{2}{5}.
  5. Find Second Solution: Now we have the two solutions: x=5x = 5 and x=−25x = -\frac{2}{5}. To enter the solutions from least to greatest, we compare the two values.
  6. Compare Solutions: Since −25-\frac{2}{5} is less than 55, the lesser xx is −25-\frac{2}{5} and the greater xx is 55.

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