The problem is to determine the number of solutions and the solutions themselves for the quadratic equation $2x^2 - 3x + 2 = 0$.

1. Problem Description

The problem is to determine the number of solutions and the solutions themselves for the quadratic equation $2x^2 - 3x + 2 = 0$.

2. Solution Steps

We can solve the quadratic equation $ax^2 + bx + c = 0$ using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this case, $a = 2$, $b = -3$, and $c = 2$.

Substituting these values into the quadratic formula, we get:

$x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(2)(2)}}{2(2)}$

$x = \frac{3 \pm \sqrt{9 - 16}}{4}$

$x = \frac{3 \pm \sqrt{-7}}{4}$

Since the discriminant ($b^2 - 4ac$) is negative ($-7$), the quadratic equation has no real solutions. It has two complex solutions, but since the answer choices are limited to real solutions, we choose the "no solution" option.

3. Final Answer

a) no solution.