Julie is solving the equation 3x2 + 5x + 15 = 0 and notices that the discriminant b2 - 4ac has a value of -155. This tells her that the equation has
.... no real solutions, but it does have 2 complex roots
two complex solutions.
The discriminant, denoted as Δ (delta), is given by the formula b^2 - 4ac. For the equation 3x^2 + 5x + 15 = 0, we can see that a = 3, b = 5, and c = 15.
Substituting these values into the discriminant formula, we have:
Δ = (5)^2 - 4(3)(15)
Δ = 25 - 180
Δ = -155
Since the discriminant is negative (-155), it tells us that the equation has two complex solutions.
To determine what the discriminant value tells us about the given equation, we need to understand the significance of the discriminant in quadratic equations.
The discriminant is the value inside the square root portion of the quadratic formula, given by the equation: Δ = b^2 - 4ac, where Δ represents the discriminant, b represents the coefficient of x, a represents the coefficient of x^2, and c represents the constant term.
Now, let's consider the discriminant value of -155 in the equation 3x^2 + 5x + 15 = 0.
Δ = b^2 - 4ac = (-155)
Since the discriminant is negative (-155), it tells us that there are no real solutions or roots for the given quadratic equation. In other words, the equation does not intersect or touch the x-axis.
So, Julie can conclude that the equation 3x^2 + 5x + 15 = 0 has no real solutions or roots, based on the negative discriminant value of -155.