Use the discriminant to determine how many real-number solutions the equation has.
s2 - 5s + 6 = 0
To determine how many real-number solutions the quadratic equation has, we can use the discriminant. The discriminant is calculated using the formula D = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In this case, the equation is s^2 - 5s + 6 = 0, so a = 1, b = -5, and c = 6. Let's calculate the discriminant:
D = (-5)^2 - 4(1)(6)
= 25 - 24
= 1
The discriminant, in this case, is 1. Now, based on the value of the discriminant, we can determine the number of real-number solutions:
1. If the discriminant is positive (D > 0), then there are two distinct real solutions.
2. If the discriminant is zero (D = 0), then there is one real solution (a repeated root).
3. If the discriminant is negative (D < 0), then there are no real solutions.
Since the discriminant here is 1 (D > 0), the equation s^2 - 5s + 6 = 0 has two distinct real-number solutions.