x^2 – 5x + 6
To work with the expression x^2 – 5x + 6, we can either factor it or solve for the roots using the quadratic formula
To work with the expression x^2 – 5x + 6, we can either factor it or solve for the roots using the quadratic formula.
1. Factoring the expression:
To factor the quadratic expression, we need to find two numbers whose product is 6 and whose sum is -5 (the coefficient of x). Those numbers are -2 and -3.
Therefore, x^2 – 5x + 6 can be factored as (x – 2)(x – 3).
2. Solve for the roots using the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 – 4ac)) / (2a)
For the given expression x^2 – 5x + 6, we have a = 1, b = -5, and c = 6.
Using the quadratic formula, we can solve for x:
x = (-(-5) ± √((-5)^2 – 4(1)(6))) / (2(1))
x = (5 ± √(25 – 24)) / 2
x = (5 ± √1) / 2
There are two possible solutions:
x = (5 + 1) / 2 = 6 / 2 = 3
x = (5 – 1) / 2 = 4 / 2 = 2
Therefore, the solutions to the quadratic equation x^2 – 5x + 6 are x = 3 and x = 2.
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