Final answer:
The discriminant of the given equation 2x² + 3x + 9 = 0 is -63.
Step-by-step explanation:
The given equation is 2x² + 3x + 9 = 0. To calculate the discriminant, we can use the formula:
Discriminant = b² - 4ac
where 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.
In this case, a = 2, b = 3, and c = 9.
Plugging in these values, we get:
Discriminant = (3)² - 4(2)(9)
Simplifying, we have:
Discriminant = 9 - 72
Discriminant = -63
Therefore, the discriminant of the equation is -63.