Respuesta :

Answer:

There are two complex roots:

  • [tex]-3\pm i[/tex]

============

Given equation:

  • x² - 6x + 10 = 0

The standard form is:

  • ax² + bx + c = 0

Compared we can find values of the coefficients and the constant:

  • a = 1, b = - 6, c = 10

Substitute these values into quadratic formula:

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

and work out roots:

    [tex]x=\dfrac{-(-6)\pm\sqrt{(-6)^2-4*1*10} }{2*1}=x=\dfrac{6\pm\sqrt{36-40} }{2}=\dfrac{6\pm2\sqrt{-1} }{2}=3 \pm i[/tex]

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