Solve the quadratic equation using the quadratic formula, x^2-3x+2=0.
looks like it factors nicely to
(x-1)(x-2) = 0
carry on
To solve the quadratic equation x^2 - 3x + 2 = 0 using the quadratic formula, we need to identify the values of a, b, and c in the general quadratic equation: ax^2 + bx + c = 0.
In this case, a = 1, b = -3, and c = 2.
The quadratic formula states that the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values of a, b, and c into the formula, we have:
x = (3 ± √((-3)^2 - 4*1*2)) / (2*1)
Simplifying further:
x = (3 ± √(9 - 8)) / 2
x = (3 ± √1) / 2
x = (3 ± 1) / 2
We have two possible solutions:
1. x = (3 + 1) / 2 = 4 / 2 = 2
2. x = (3 - 1) / 2 = 2 / 2 = 1
Therefore, the solutions to the quadratic equation x^2 - 3x + 2 = 0 are x = 2 and x = 1.