By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.
Let be a quadratic function of the form a · x² + b · x + c = 0, whose roots can be found by means of the following formula:
[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex] (1)
Where a, b, c are the coefficients of the quadratic function.
In we know that 2 · x² - 2 · x + 5 = 0, then the roots of the polynomial are, respectively:
[tex]x_{1} = \frac{2 + \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]
[tex]x_{1} = \frac{2 + \sqrt{4-40}}{4}[/tex]
x₁ = 0.5 + i 1.5
[tex]x_{2} = \frac{2 - \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]
[tex]x_{2} = \frac{2 - \sqrt{4-40}}{4}[/tex]
x₂ = 0.5 - i 1.5
By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.
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