solve the equation:
x^2-x+2=0
is 1+9i/2 the correct answer?
No, that is not the answer I get when I plug in to the quadratic formula.
I get
(1 + sqrt7i)/2
and
(1 - sqrt7i)/2
Do you understand how I got this?
Where does the seven come from?
sqrt(b^2 - 4ac).
b is -1 and a is 1 and c is 2.
So, sqrt(b^2 - 4ac) is
sqrt(-7), or (sqrt7)i.
ohhhh! okay thank you!
You're welcome
To solve the equation x^2 - x + 2 = 0, you can use the quadratic formula or factorization method.
Using the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, a = 1, b = -1, and c = 2. Plugging these values into the quadratic formula, we get:
x = (1 ± √((-1)^2 - 4(1)(2))) / (2(1))
x = (1 ± √(1 - 8)) / 2
x = (1 ± √(-7)) / 2
Here, we notice that we have a negative value under the square root, which means that the equation does not have real solutions. Instead, it has complex solutions.
So, the solution of the equation x^2 - x + 2 = 0 is x = (1 ± √(-7)) / 2.
Now, let's check if 1 + 9i/2 is a correct solution.
Substituting this value into the equation:
(1 + 9i/2)^2 - (1 + 9i/2) + 2 = 0
Expanding and simplifying, we get:
1 + 9i + 81i^2/4 - 1 - 9i/2 + 2 = 0
81i^2/4 = -81/4
Here, i^2 = -1, so:
81(-1)/4 = -81/4
So, the left side of the equation does not equal zero. Therefore, 1 + 9i/2 is not a correct solution to the equation x^2 - x + 2 = 0.