The discriminant of a quadratic equation is calculated using the formula D = b² – 4ac, where a, b, and c are the coefficients of the equation in the standard form ax² + bx + c = 0.
In the given equation, 2x² + 3x + 5 = 0, we identify the coefficients as follows:
- a = 2
- b = 3
- c = 5
Now, plug these values into the discriminant formula:
D = 3² – 4(2)(5)
Calculating this gives:
- D = 9 – 40
- D = -31
So, the discriminant for the quadratic equation 2x² + 3x + 5 = 0 is -31. This negative value indicates that the equation has no real roots, meaning the solutions are complex numbers.