Question

The function f(x) = 2x^2 + 3x + 5, when evaluated, gives a value of 19. What is the function’s input value?
a. 1
b. -1
c. 2
d. -2
e. -3

Answer 1

$f(x)=19 \\ 2x^2+3x+5=19 \\ 2x^2+3x+5-19=0 \\ 2x^2+3x-14=0 \\ 2x^2-4x+7x-14=0 \\ 2x(x-2)+7(x-2)=0 \\ (2x+7)(x-2)=0 \\ 2x+7=0 \ \lor \ x-2=0 \\ 2x=-7 \ \lor \ x=2 \\ x=-\frac{7}{2} \ \lor \ x=2$

The value of the function is 19 for x=-7/2 or x=2.
The answer is C.