Answer:
Explanation:
To determine the character of the solutions of the equation in the complex number system, we need to analyze the nature of the coefficients of the equation, specifically the discriminant, which is obtained by the equation: b^2 - 4ac, where a, b and c are the coefficients of the equation.
In this case, the equation is
3x^2 + 7x - 3 = 0
So, the coefficients are a = 3, b = 7, and c = -3.
We can now calculate the discriminant as follows:
b^2 - 4ac = 7^2 - 4 * 3 * -3 = 49 + 36 = 85
Since the discriminant is positive, we know that the equation has two distinct real solutions. The exact solutions can be obtained using the quadratic formula, but that's not required to determine the character of the solutions.
Therefore, the equation has two real solutions.