To solve the equation 0 = 3x² + x + 4, we can analyze the quadratic equation in the standard form ax² + bx + c.
Here, a = 3, b = 1, and c = 4. To determine the number of real solutions, we can use the discriminant, which is given by the formula D = b² – 4ac.
Substituting the values, we get the discriminant:
D = (1)² – 4(3)(4) = 1 – 48 = -47
Since the discriminant is negative (-47), this indicates that there are no real number solutions to the equation. In other words, the quadratic graph does not intersect the x-axis, meaning the equation has two complex solutions instead.
In conclusion, the equation 0 = 3x² + x + 4 has zero real number solutions.