Answer
The equation has two unequal real solutions.
Work Step by Step
The equation has $a=2, b=-4, \text{ and } c=1$.
To determine the character of the solutions of this equation, we need to find the value of its discriminant which is $b^2 - 4ac$.
Substitute the values into this expression:
$b^2 - 4ac = (-4)^2 - 4(2)(1)$
$b^2 - 4ac = 16 - 4(2)(1)$
$b^2 - 4ac = 16 - 8$
$b^2 - 4ac = 8$
Since $8 > 0$, the equation has two unequal real solutions.
