Is this correct:
solve using the quadratic equation:
5x^-4x+1=0
My answer:
x= (2)/(5) +/- (1)/(5)i
Or should i combine the denominators to look like this:
x= (2+/-1)/(5) i
I don't like where you show the i
I would write the solution as
(2 +-i)/5 or 2/5 +-i/5
To solve the quadratic equation 5x^2 - 4x + 1 = 0, you can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions (or roots) can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For the given equation, a = 5, b = -4, and c = 1. Substituting these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)^2 - 4(5)(1))) / (2(5))
Simplifying this expression, we have:
x = (4 ± √(16 - 20)) / 10
x = (4 ± √(-4)) / 10
Now, we encounter a square root of a negative number, which is not a real number. In mathematics, the imaginary unit is denoted as i, where i^2 = -1. Therefore, we can rewrite the expression as:
x = (4 ± 2i) / 10
x = (2 ± i) / 5
Using the fractional form, we can express it as:
x = 2/5 ± i/5
So, your initial answer is correct; x = (2/5) ± (1/5)i. However, you prefer to combine the denominators. In that case, you can rewrite it as:
x = (2 ± 1) / 5i
x = (2 ± 1)/5i
Alternatively, you can write it as:
x = (2 ± i) / 5
Both forms are acceptable, and it's a matter of personal preference.