This is the problem you helped me with. I was curious, do I write the solution set as (1 + i3�ã3)/2,
(1-i3�ã3)/2
change it to the standard form first
x^2 - x + 7 = 0
a=1, b=-1, c = 7
x = (1 �} �ã(1 - 4(1)(7))/2
= (1 �} �ã-27)/2
Your answer is an imaginary number or called a complex number, you could rewrite is as
x = (1 �} 3�ã3 i)/2
Yes, the solution set for the quadratic equation x^2 - x + 7 = 0 is indeed in the form of complex numbers. To convert it to the standard form, let's go through the steps.
Given equation: x^2 - x + 7 = 0
We can identify the coefficients as:
a = 1 (coefficient of x^2)
b = -1 (coefficient of x)
c = 7 (constant term)
To find the solutions, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
x = (1 ± √((-1)^2 - 4(1)(7))) / (2(1))
x = (1 ± √(1 - 28)) / 2
x = (1 ± √(-27)) / 2
At this point, the discriminant (b^2 - 4ac) is negative, leading to imaginary solutions. To simplify the expression, we can rewrite the radical as √(-1) * √(27) = i√(27) = i√(3*9) = i√3√9 = 3i√3.
So we have:
x = (1 ± 3i√3) / 2
Lastly, we can split the expression into two separate solutions by using the ± sign:
x1 = (1 + 3i√3) / 2
x2 = (1 - 3i√3) / 2
Therefore, the solution set in standard form is:
x = (1 + 3i√3) / 2, (1 - 3i√3) / 2
Note: The numerator in your original expression (1 + i3√3) should be (1 + 3i√3).