Julie is solving the equation x2 + 6x + 9 = 0 and notices that the discriminant b2 - 4ac has a value of 0. This tells her that the equation has
two equal roots
The discriminant of a quadratic equation is the expression b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, Julie has the equation x^2 + 6x + 9 = 0, so we can identify the values of a, b, and c.
a = 1
b = 6
c = 9
Now we can substitute these values into the formula for the discriminant:
b^2 - 4ac = 6^2 - 4(1)(9) = 36 - 36 = 0
The fact that the discriminant is equal to 0 tells us information about the nature of the solutions of the quadratic equation.
If the discriminant is equal to 0, it means that the quadratic equation has exactly one real solution. This happens when the equation has a perfect square trinomial, which means that it can be factored as (x + k)^2 = 0.
In Julie's case, the equation x^2 + 6x + 9 = 0 can be factored as (x + 3)^2 = 0. This means that the only solution for the equation is x = -3.