Solve this

Question:

$2 x^{2}-4 x+3=0$

 

Solution:

Given:

$2 x^{2}-4 x+3=0$

Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:

$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$

$\Rightarrow x=\frac{-(-4) \pm \sqrt{(-4)^{2}-(4 \times 2 \times 3)}}{2 \times 2}$

$\Rightarrow x=\frac{4 \pm \sqrt{16-24}}{4}$

$\Rightarrow x=\frac{4 \pm \sqrt{-8}}{4}$

$\Rightarrow x=\frac{4 \pm 2 \sqrt{2} i}{4}$

$\Rightarrow x=\frac{4}{4} \pm \frac{2 \sqrt{2}}{4} i$

$\Rightarrow \quad x=1 \pm \frac{i}{\sqrt{2}}$

Ans: $x=1+\frac{i}{\sqrt{2}}$ and $x=1-\frac{i}{\sqrt{2}}$

 

 

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