Final answer:
The other zero of the function is (-3, 0).
Step-by-step explanation:
To find the other zero of the function, we need to solve for x in the equation f(x) = 2x^2 + x - 15 = 0. Since we already know that one of the zeros is (2.5, 0), we can use this information to solve for the other zero.
First, we can set x = 2.5 in the equation and solve for f(x):
f(2.5) = 2(2.5)^2 + 2.5 - 15
= 2(6.25) + 2.5 - 15
= 12.5 + 2.5 - 15
= 0
We can see that f(2.5) = 0, which means that (2.5, 0) is a point on the graph of the function. This is also one of the zeros of the function, as given in the question.
Now, we can use the quadratic formula to find the other zero of the function. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 2, b = 1, and c = -15. Substituting these values in the formula, we get:
x = (-1 ± √(1^2 - 4(2)(-15))) / 2(2)
= (-1 ± √(1 + 120)) / 4
= (-1 ± √121) / 4
= (-1 ± 11) / 4
Therefore, the two possible values for x are:
x = (-1 + 11) / 4 = 10/4 = 2.5
x = (-1 - 11) / 4 = -12/4 = -3
Since we already know that x = 2.5 is one of the zeros, the other possible value is x = -3. This means that the other zero of the function is (-3, 0).