Final answer:
The quadratic equation x²-5x+1=0 is solved using the quadratic formula yielding two solutions: x = (5 - √21) / 2 and x = (5 + √21) / 2.
Step-by-step explanation:
To solve the quadratic equation x²-5x+1=0 using the quadratic formula, we first identify the coefficients a, b, and c in the equation ax² + bx + c = 0. Here, a = 1, b = -5, and c = 1. The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). Substituting the values into the formula gives:
x = (-(-5) ± √((-5)² - 4(1)(1))) / (2(1))
x = (5 ± √(25 - 4)) / 2
x = (5 ± √(21)) / 2
Thus, the solutions are:
- x = (5 - √21) / 2
- x = (5 + √21) / 2
The correct answers are x = (5 - √21) / 2 and x = (5 + √21) / 2.