Final answer:
The quadratic equation 2x² + x + 11 = 0 has no real solutions because the discriminant is negative, indicating two complex solutions.
Step-by-step explanation:
To identify the number and type of solutions for the equation 2x² + x + 11 = 0, we can use the discriminant, which is part of the quadratic formula. For a quadratic equation of the form ax²+bx+c = 0, the discriminant is b² - 4ac. In this equation, a = 2, b = 1, and c = 11. Plugging these into the discriminant gives us:
Discriminant = (1)² - 4(2)(11) = 1 - 88 = -87
Since the discriminant is less than zero, this indicates that the quadratic equation has no real solutions; instead, it has two complex solutions.
The given equation is 2x² + x + 11 = 0.
To identify the number and type of solutions, we can use the discriminant formula: D = b² - 4ac.
In this equation, a = 2, b = 1, and c = 11.
Substituting these values into the discriminant formula, we get D = (1)² - 4(2)(11) = 1 - 88 = -87.
Since the discriminant is negative, the equation has two complex solutions.