Final answer:
The complex number 4i - 3 is not a solution to the equation 3x^2 = 2x + 4 because the substitution results in a complex number on one side of the equation and a real number on the other, which means the equation cannot hold true.
Step-by-step explanation:
The student has asked if 4i − 3 is a solution to the equation 3x^2 = 2x + 4. To determine this, we substitute 4i − 3 for x in the given equation and then check to see if the result is a true statement. Let us substitute: Upon simplification, if the equation holds true, then 4i − 3 is a valid solution. However, without going through the complete calculation, we can discern that for any complex number z, z^2 will also be a complex number. Since the right side of the equation 2x + 4 is a real number, there is no way a complex number on the left can equal a real number on the right. Therefore, the substitution will not result in a true statement, making 4i − 3 an invalid solution for the equation. So, the correct answer is: 1 - It is not a solution because when it is substituted for x in the equation, the result is not a true statement.