Answer:
Explanation:
The given expression is 4x^2 - 6x + 3.
To find the factors of this expression, we need to factorize it. However, we notice that it cannot be factored using real numbers. Therefore, we can use the quadratic formula to find the solutions.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our expression, a = 4, b = -6, and c = 3.
We can substitute these values into the quadratic formula:
x = (-(-6) ± √((-6)^2 - 4(4)(3))) / (2(4))
x = (6 ± √(36 - 48)) / 8
x = (6 ± √(-12)) / 8
x = (6 ± √(-1 * 12)) / 8
x = (6 ± √(-1) * √(12)) / 8
x = (6 ± 2i√3) / 8
So, the solutions are:
x = (6 + 2i√3) / 8
x = (6 - 2i√3) / 8
Since the expression cannot be factored using real numbers, the factors of the expression are (x - (6 + 2i√3) / 8) and (x - (6 - 2i√3) / 8).