Solve 3x² - 2x + 1 = 0. Give the real part and the positive imaginary part of the roots to 3…

Step 1. The discriminant. $D = (-2)^2 - 4 \times 3 \times 1 = -8$.

Step 2. The roots. $x = \dfrac{2 \pm 2\sqrt{2}\,i}{6} = \dfrac{1 \pm \sqrt{2}\,i}{3}$.

Step 3. The decimals. $\dfrac{1}{3} \approx 0.333$ and $\dfrac{\sqrt{2}}{3} \approx 0.471$.

Step 4. Check. The product is $\dfrac{1 + 2}{9} = \dfrac{1}{3} = \dfrac{c}{a}$.