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

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Determine end behavior of polynomial and rational functions

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Q. Find the zeros of the function. Enter the solutions from least to greatest.

f(x)=(x-5)(5x+2)

Set Function Equal to Zero: To find the zeros of the function, we need to set the function equal to zero and solve for $x$ . $f(x) = (x - 5)(5x + 2) = 0$ We have a product of two factors equal to zero, which means that at least one of the factors must be zero.
Solve for First Factor: We set the first factor equal to zero and solve for $x$ . $x - 5 = 0$ Adding $5$ to both sides gives us: $x = 5$
Solve for Second Factor: Now we set the second factor equal to zero and solve for $x$ . $5x + 2 = 0$ Subtracting $2$ from both sides gives us: $5x = -2$ Dividing both sides by $5$ gives us: $x = -\frac{2}{5}$
Identify Zeros: We have found the two values of $x$ that make the function equal to zero. These are the zeros of the function. $\newline$ The zeros are $x = 5$ and $x = -\frac{2}{5}$ . $\newline$ We should now order these from least to greatest.
Order Zeros: Ordering the zeros from least to greatest, we get: $x = -\frac{2}{5}$ and $x = 5$

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