How many real number solutions are there to the equation 0 = –3x² + x – 4?

Question

A. 0
B. 1
C. 2
D. 3

Answer 1

Using the quadratic formula, we have:

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Plugging in $a=-3$, $b=1$, and $c=-4$, we get:

$$x=\frac{-1\pm\sqrt{1-4(-3)(-4)}}{2(-3)}$$

Simplifying:

$$x=\frac{-1\pm\sqrt{49}}{-6}$$

So the solutions are:

$$x=\frac{1}{3} \quad \text{and} \quad x=-\frac{4}{3}$$

Therefore, the answer is $\boxed{\textbf{(C) }2}$.