Question #N161
The function *f* is defined by *f*(x) = 2x^2 - 3x + 1. If *f*(a) = 10, what is the value of *a*?
A. -2
B. -1
C. 1
D. 2
Correct Answer is: D
We substitute 10 for *f*(a) in the equation *f*(x) = 2x^2 - 3x + 1 to get 10 = 2a^2 - 3a + 1. Subtracting 10 from both sides gives 0 = 2a^2 - 3a - 9. Factoring the right-hand side, we get 0 = (2a + 3)(a - 3). Setting each factor equal to 0, we get 2a + 3 = 0, which gives a = -3/2, or a - 3 = 0, which gives a = 3. Of these, only 3 is a choice, so the answer is 3.