how many real-number solutions does the equation have?
0=3x^2+18x+27
To find the number of real-number solutions for the equation 0=3x^2+18x+27, we can use the discriminant formula. The discriminant, denoted as Δ, is given by the formula Δ = b^2 - 4ac.
In the equation 0=3x^2+18x+27, the coefficients are a = 3, b = 18, and c = 27.
Substituting these values into the discriminant formula, we get:
Δ = (18)^2 - 4(3)(27)
= 324 - 324
= 0
Since the discriminant Δ is equal to 0, this means that the equation has exactly one real-number solution (because Δ = 0 corresponds to the case of one real root).