Final answer:
To determine the number of solutions of the given quadratic equation -4x² +4x-3=0, calculate the discriminant. With coefficients a=-4, b=4, c=-3, we find that the discriminant is negative (-32), meaning the equation has two complex solutions.
Step-by-step explanation:
The question you're asking is how to determine the number of solutions for the quadratic equation -4x² +4x-3=0. In general, the number of solutions of a quadratic equation can be determined by calculating the discriminant, which is found using the formula b² - 4ac, where the coefficients a, b, and c correspond to the quadratic equation in the form ax²+bx+c = 0.
To apply this to the given equation:
- Identify the coefficients a = -4, b = 4, and c = -3.
- Compute the discriminant: (4)2 - 4(-4)(-3).
- Analyze the discriminant value:
- If it is positive, there are two real solutions.
- If it is zero, there is one real solution.
- If it is negative, there are two complex solutions.
In this case, the discriminant computation would be 16 - 4(-4)(-3) = 16 - 48 = -32. Since the discriminant is negative, the quadratic equation has two complex solutions.