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3x2-6x+5=0

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Answer:

[tex]\sf x=1+i\sqrt{\dfrac{2}{3}} \ \quad and \quad \:x=1-i\sqrt{\dfrac{2}{3}}[/tex]

Explanation:

Given Expression:

  • 3x² - 6x + 5 = 0

Use the Quadratic Formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ \ ax^2 + bx + c = 0[/tex]

insert coefficients

[tex]\Longrightarrow \sf x = \dfrac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:3\cdot \:5}}{2\cdot \:3}[/tex]

[tex]\Longrightarrow \sf x = \dfrac{\left6\right\pm \sqrt{-24} }{6}[/tex]

[tex]\Longrightarrow \sf x = \dfrac{\left6\right\pm 2\sqrt{6}i}{6}[/tex]

[tex]\Longrightarrow \sf x =1 \pm i\dfrac{\sqrt{6} }{3}[/tex]

[tex]\Longrightarrow \sf x=1+i\sqrt{\dfrac{2}{3}}, \quad 1-i\sqrt{\dfrac{2}{3}}[/tex]
  • 3x²-6x+5=0

Use quadratic formula

[tex]\\ \rm\Rrightarrow x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{6\pm \sqrt{36-60}}{6}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{6\pm\sqrt{-24}}{6}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{6\pm2\sqrt{6}i}{6}[/tex]

[tex]\\ \rm\Rrightarrow x=1\pm \dfrac{sqrt{2}i}{\sqrt{3}}[/tex]

[tex]\\ \rm\Rrightarrow x=1\pm\sqrt{\dfrac{2}{3}}i[/tex]

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