Given 27x2 – 10x + 1 = 0
Recall that the roots of quadratic equation ax2 + bx + c = 0, where a ≠ 0, are given by
We have i2 = –1
By substituting –1 = i2 in the above equation, we get
Thus, the roots of the given equation are \(\frac{5}{27}±\frac{\sqrt{2}}{27}\) i.