Question #N476
The function *f* is defined by *f*( *x* ) = *x*<sup>2</sup> + *x* - 2. If *f*( *a* ) = 10, what is the value of *a*?
A. -4
B. -3
C. 3
D. 4
Correct Answer is: C
We can solve for *a* by substituting 10 for *f*( *a* ) in the equation and then solving the quadratic equation. This gives us 10 = *a*<sup>2</sup> + *a* - 2. Subtracting 10 from both sides of this equation, we get 0 = *a*<sup>2</sup> + *a* - 12. Factoring the quadratic expression, we get ( *a* + 4 )( *a* - 3 ) = 0. The solutions are *a* = -4 and *a* = 3. The value of *a* = 3 is the one that satisfies the given condition, so the answer is 3.