Solve the following quadratics $27 x^{2} - 10 x + 1 = 0$

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Solution

$27 x^{2} - 10 x + 1 = 0 We will discriminant rule, x = \frac{- b \pm \sqrt{D}}{2 a} . . . (A) w h e r e D = b^{2} - 4 a c = (- 10)^{2} - 4.27.1 = 100 - 108 = - 8 f r o m (A) x = \frac{- (- 10) \pm \sqrt{- 8}}{54} = \frac{10 \pm 2 \sqrt{2 i}}{54} = \frac{5 \pm \sqrt{2 i}}{27} ∴ x = \frac{5}{27} + \frac{\sqrt{2 i}}{27}, \frac{5}{27} - \frac{\sqrt{2}}{27} i$

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