Final answer:
To find the roots of the given quadratic equation, X² - 5x + 4 = 0, we can use the quadratic formula. The roots are x = 4 and x = 1, rounded to two decimal places.
Step-by-step explanation:
To find the roots of the given quadratic equation, X² - 5x + 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b² - 4ac)) / (2a)
In our equation, a = 1, b = -5, and c = 4. Plugging these values into the formula, we get:
x = (-(-5) ± √((-5)² - 4(1)(4))) / (2(1))
Simplifying further:
x = (5 ± √(25 - 16)) / 2
x = (5 ± √9) / 2
x = (5 ± 3) / 2
Therefore, the two roots of the equation are:
x = (5 + 3) / 2 = 8 / 2 = 4
x = (5 - 3) / 2 = 2 / 2 = 1
So the roots of the equation X² - 5x + 4 = 0 are x = 4 and x = 1, rounded to two decimal places.