Answer:
Number of solutions: 0
Type of solutions: Nonreal
Explanation:
Identifying the form of 2x^2 - 2x + 3 = 0
2x^2 - 2x + 3 = 0 is in the standard form of a quadratic, whose general equation is given by:
ax^2 + bx + c = 0, where
- a, b, and c are constants.
Thus, 2 is our a value, -2 is our b value, and 3 is our c value.
Using the discriminant to determine the number and type of solutions:
The discriminant (D) comes from the quadratic formula and is given by:
D = b^2 - 4ac
The discriminant can reveal three things about the number and type of solutions:
- When D < 0, there are 0 real solutions.
- When D = 0, there is 1 real solution.
- When D > 0, there are 2 real solutions.
Thus, we can plug in -2 for b, 2 for a, and 3 for c in the discriminant equation to determine the number and type of solutions for 2x^2 - 2x + 3 = 0:
D = (-2)^2 - 4(2)(3)
D = 4 -24
D = -20
Since -20 is less than 0, there are 0 real solutions.