Answer:
[tex]x = \frac{ 1 + 1\sqrt{-1}}{3}[/tex] and [tex]x = \frac{ 1 - 1\sqrt{-1}}{3}[/tex]
Step-by-step explanation:
Hello!
The quadratic formula is: [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex], derive from the standard form of a quadratic: [tex]ax^2 + bx + c[/tex].
The expression 3x² - 2x + 1 is a lot like our standard form:
Let's plug in the values and solve.
Solve the Quadratic Formula:
- [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
- [tex]x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(2)(1)}}{2(3)}[/tex]
- [tex]x = \frac{2 \pm\sqrt{4 - 8}}{6}[/tex]
- [tex]x = \frac{2 \pm \sqrt{-4}}{6}[/tex]
- [tex]x = \frac{2 \pm 2\sqrt{-1}}{6}[/tex]
- [tex]x = \frac{ 1 \pm 1\sqrt{-1}}{3}[/tex]
The roots are [tex]x = \frac{ 1 + 1\sqrt{-1}}{3}[/tex] and [tex]x = \frac{ 1 - 1\sqrt{-1}}{3}[/tex]
Learn more about the derivation of the quadratic formula here:
https://brainly.com/question/11630991
