Final answer:
The equation x²-5x+7=0 has two complex solutions, which are calculated using the quadratic formula. These solutions are x = 2.5 + (√3/2)i and x = 2.5 - (√3/2)i.
Step-by-step explanation:
To find the solutions of the quadratic equation x²-5x+7=0, we can use the quadratic formula, which is applicable to equations of the form ax²+bx+c=0. The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a=1, b=-5, and c=7. Plugging these values into the formula gives us:
x = (5 ± √((-5)² - 4(1)(7))) / (2(1))
x = (5 ± √(25 - 28)) / 2
Since the discriminant (25 - 28) is negative, this means we will have two complex solutions. Let's calculate these:
x = (5 ± √(-3)) / 2
x = (5 ± √3i) / 2
Therefore, the solutions are:
x = 2.5 + (√3/2)i and x = 2.5 - (√3/2)i