What mathematical function has zeros at x = 2 and x = 5?

To find a function that has zeros at specific x-values, you can use the fact that a function is equal to zero at those points. In this case, we’re looking for a function that is equal to zero when x = 2 and x = 5.

In polynomial functions, zeros correspond to the factors of the equation. Therefore, if we have zeros at x = 2 and x = 5, we can express the function in factored form as:

f(x) = (x – 2)(x – 5)

When you expand this polynomial, you can find the standard form:

f(x) = x² – 5x – 2x + 10 = x² – 7x + 10

Thus, the function f(x) = (x – 2)(x – 5) has zeros at x = 2 and x = 5. You can visualize this function by plotting it on a graph; it will intersect the x-axis at these two points, demonstrating its roots.

In conclusion, if you are looking for a polynomial function that has zeros at x = 2 and x = 5, a good choice is:

f(x) = (x – 2)(x – 5) or f(x) = x² – 7x + 10.

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