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Find the zeros of the function. Enter the solutions from least to greatest. f(x)=(x−5)(5x+2) f(x)=(x-5)(5x+2)

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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. f(x)=(x−5)(5x+2) f(x)=(x-5)(5x+2)
  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.f(x)=(x−5)(5x+2)=0f(x) = (x - 5)(5x + 2) = 0We have a product of two factors equal to zero, which means that at least one of the factors must be zero.
  2. Solve for First Factor: We set the first factor equal to zero and solve for xx.x−5=0x - 5 = 0Adding 55 to both sides gives us:x=5x = 5
  3. Solve for Second Factor: Now we set the second factor equal to zero and solve for xx.5x+2=05x + 2 = 0 Subtracting 22 from both sides gives us:5x=−25x = -2 Dividing both sides by 55 gives us:x=−25x = -\frac{2}{5}
  4. Identify Zeros: We have found the two values of xx that make the function equal to zero. These are the zeros of the function.\newlineThe zeros are x=5x = 5 and x=−25x = -\frac{2}{5}.\newlineWe should now order these from least to greatest.
  5. Order Zeros: Ordering the zeros from least to greatest, we get: x=−25x = -\frac{2}{5} and x=5x = 5

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