Which of these equations represents a quadratic equation with two real solutions?

Which of these equations represents a quadratic equation with two real solutions?

• A. x² + 5x + 6 = 0
• B. x² + 2x + 3 = 0
• C. x² + 1x - 2 = 0
• D. x² + 4x + 4 = 0

Answer: (A)

To determine if a quadratic equation has two real solutions, we can use the discriminant, which is part of the quadratic formula. The discriminant is given by the formula \(D = b^2 - 4ac\), where \(a\), \(b\), and \(c\) are the coefficients of the quadratic equation in the standard form \(ax^2 + bx + c = 0\). For the equation \(x^2 + 5x + 6 = 0\): 1. Identify the coefficients: \(a = 1\), \(b = 5\), and \(c = 6\). 2. Calculate the discriminant: \[ D = b^2 - 4ac = 5^2 - 4(1)(6) = 25 - 24 = 1. \] Since the discriminant \(D = 1\) is greater than zero, this indicates that the quadratic equation has two distinct real solutions. In contrast, for the other equations: - The equation \(x^2 + 2x + 3 = 0\) has a negative discriminant (\(D < 0\)), resulting in complex solutions

To determine if a quadratic equation has two real solutions, we can use the discriminant, which is part of the quadratic formula. The discriminant is given by the formula (D = b^2 - 4ac), where (a), (b), and (c) are the coefficients of the quadratic equation in the standard form (ax^2 + bx + c = 0).

For the equation (x^2 + 5x + 6 = 0):

1. Identify the coefficients: (a = 1), (b = 5), and (c = 6).

2. Calculate the discriminant:

[

D = b^2 - 4ac = 5^2 - 4(1)(6) = 25 - 24 = 1.

]

Since the discriminant (D = 1) is greater than zero, this indicates that the quadratic equation has two distinct real solutions.

In contrast, for the other equations:

• The equation (x^2 + 2x + 3 = 0) has a negative discriminant ((D < 0)), resulting in complex solutions