Question

Choose the best description of the roots of the equation 3x 2 - 4x + 5 = 0.

Answer 1

For this case we have the following polynomial:
 $3x ^ 2 - 4x + 5 = 0$
 Using the resolver we have:
 $x = \frac{-b +/- \sqrt{b^2 - 4ac}}{2a}$
 Substituting values we have:
 $x = \frac{-(-4) +/- \sqrt{(-4)^2 - 4*3*5}}{2*3}$
 $x = \frac{4 +/- \sqrt{16 - 60}}{6}$
 $x = \frac{4 +/- \sqrt{-44}}{6}$
 $x = \frac{4 +/- \sqrt{-4*11}}{6}$
 $x = \frac{4 +/- 2\sqrt{-11}}{6}$
 $x = \frac{2 +/- \sqrt{-11}}{3}$
 $x = \frac{2 +/- i\sqrt{11}}{3}$
 Answer:
 We observe that the solution to the quadratic equation are two imaginary roots.