# Chapter 1 - Test - Page 147: 7

The equation has no real solutions. (Complex solutions: $\frac{1\pm\sqrt{11}i}{6}$)

#### Work Step by Step

$3x^{2}-x+1=0$ We solve using the quadratic formula ($a=3,\ b=-1,\ c=1$): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $x=\displaystyle \frac{-(-1)\pm\sqrt{(-1)^{2}-4*3*1}}{2*3} =\displaystyle \frac{1\pm\sqrt{-11}}{6}=\frac{1\pm\sqrt{11}i}{6}$ However, we note that the discriminant is negative. Therefore, the equation has no real solutions.

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