Question

Solve the equation :
${27x}^2-10x+1=0$

Answer 1

The given quadratic equation is ${27x}^2-10x+1=0$
On comparing this equation with ${ax}^2+bx+c=0$,
we obtain $a=27,b=-10,$ and $c=1$
Therefore, the discriminant of the given equation is
$D=b^2-4ac={(-10)}^2-4\times 27\times 1=100-108=-8$
Therefore, the required solutions are
$\frac{-b\pm \sqrt{D}}{2a}=\frac{-(-10)\pm \sqrt{-8}}{2\times 27}=\frac{10\pm 2\sqrt{2}i}{54}$
$=\frac{5\pm \sqrt{2}i}{27}=\frac{5}{27}\pm \frac{\sqrt{2}}{27}i$