Answer:
[tex]x_{1} = -\frac{1}{3} +\sqrt{2} ; x_{2} = -\frac{1}{3}-\sqrt{2}[/tex]
Step-by-step explanation:
9x² + 6x – 17 = 0
Apply the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = 9; b = 6; y = -17
[tex]x = \frac{-6\pm\sqrt{6^2 - 4\times 9 \times(-17)}}{2\times 9}[/tex]
[tex]x = \frac{-6\pm\sqrt{36+36\times17}}{18}[/tex]
[tex]x = \frac{-6\pm\sqrt{36(1+17)}}{18}[/tex]
[tex]x = \frac{-6\pm 6 \sqrt{18}}{18}[/tex]
[tex]x = \frac{-1\pm \sqrt{9\times2}}{3}[/tex]
[tex]x = \frac{-1\pm 3\sqrt{2}}{3}[/tex]
[tex]x_{1} = -\frac{1}{3} +\sqrt{2} ; x_{2} = -\frac{1}{3}-\sqrt{2}[/tex]
The graph below shows the roots at x₁ =1.081 and x₂ = -1.748.
