To find the number of real number solutions to the equation 3x² + 4 = 0, we can start by rearranging the equation:
3x² = -4
Next, we divide both sides by 3:
x² = -\frac{4}{3}
Now, we can see that we have x² equal to a negative number. In real numbers, the square of any real number is always non-negative (greater than or equal to 0). Therefore, there are no real numbers that can satisfy this equation, since a square cannot equal a negative value.
Based on this analysis, we can conclude that the equation 3x² + 4 = 0 has zero real number solutions.