Finding Zeros of the Function \(f(x) = (x - 17)(x - 7)\)
The zeros of a function are the input values (\(x\)) that make the function's output (\(f(x)\)) equal to zero. To find the zeros of \(f(x) = (x - 17)(x - 7)\), we need to solve the equation \(f(x) = 0\).
Step-by-Step Solution
- Set the function equal to zero: \((x - 17)(x - 7) = 0\)
- Apply the zero product property. If the product of two factors is zero, then at least one of the factors must be zero.
- Set the first factor to zero: \(x - 17 = 0\)
- Set the second factor to zero: \(x - 7 = 0\)
- Solve for \(x\) in each case:
- From \(x - 17 = 0\), we get \(x = 17\).
- From \(x - 7 = 0\), we get \(x = 7\).
Therefore, the zeros of the function \(f(x) = (x - 17)(x - 7)\) are 17 and 7.
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