Gujarat BoardEnglish MediumSTD 11 ScienceMATHSCOMPLEX NUMBERS AND QUADRATIC EQUATIONS2 Marks
Question
Solve $x^2 + x + \frac{1}{{\sqrt 2}} = 0$
✓
Answer
Here, ${x^2} + x + \frac{1}{{\sqrt 2}} = 0$
Comparing the given quadratic equation with $ax^2 + bx + c = 0$ we have
$a = 1, b =1$ and $c = \frac{1}{{\sqrt 2}}$
$\therefore x = \frac{-1\pm\sqrt{1-2\sqrt2}}{2} = \frac{-1 \pm\sqrt{\left(2\sqrt{2 }-1\right)}i}{2}$
Thus, $x = \frac{-1 +\sqrt{\left(2\sqrt{2 }-1\right)}i}{2} \ x = \frac{-1 - \sqrt{\left(2\sqrt{2 }-1\right)}i}{2}$
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