Show the following quadratic equation by factorization method: x^… - Vidyadip

Question

Show the following quadratic equation by factorization method: $x^2 - x + 1 = 0$

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Answer

$x^2 - x + 1 = 0$ Now, completing the squares, we get $\Big(\text{x}+\frac{1}{2}\Big)^2+\frac{3}{4}=0$ $\Rightarrow\Big(\text{x}+\frac{1}{2}\Big)^2-\Big(\frac{\sqrt{3}}{2}\text{i}\Big)^2=0$ $\Rightarrow\Big(\text{x}+\frac{1}{2}+\frac{\sqrt{3}}{2}\text{i}\Big)\Big(\text{x}+\frac{1}{2}-\frac{\sqrt{3 }}{2}\text{i}\Big)=0$ $\Rightarrow\Big(\text{x}+\frac{1}{2}+\frac{\sqrt{3}}{2}\text{i}\Big)=0\ \text{or } \Big(\text{x}+\frac{1}{2}-\frac{\sqrt{3}}{2}\text{i}\Big)=0$ $\therefore\text{x}=\frac{-1}{2}+\frac{-1}{2}+\frac{\sqrt{3}}{2}\text{ i},\frac{-1}{2}-\frac{\sqrt{3}}{2}\text{ i}$

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