To find a function that has zeros at x = 2 and x = 5, we can construct a polynomial function from these roots. The simplest form of such a function is to write it in factored form:
f(x) = (x – 2)(x – 5)
Now, let’s expand this expression:
f(x) = x² – 5x – 2x + 10 = x² – 7x + 10
Thus, the polynomial function f(x) = x² – 7x + 10 has zeros at x = 2 and x = 5. This means that when you plug in these values for x, the output of the function will be zero, confirming that these are indeed the roots of the function.