Gujarat BoardEnglish MediumSTD 11 ScienceMATHSCOMPLEX NUMBERS AND QUADRATIC EQUATIONS4 Marks
Question
Solve the following equation: $\sqrt{3}\text{x}^2-\sqrt{2}\text{x}+3\sqrt{3}=0.$
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Answer
The given quadratic equation is $\sqrt{3}\text{x}^2-\sqrt{2}\text{x}+3\sqrt{3}=0$ On comparing the given equation with $ax^2 + bx + c = 0$, we obtain $\text{a}=\sqrt{3},\text{ b}=-\sqrt{2},\ \text{and c}=3\sqrt{3}$ Therefore, the discriminant of the givenequation is $\text{D}=\text{b}^2-4\text{ac}$ $=(-\sqrt{2})^2-4(\sqrt{3})(3\sqrt{3})=2-36=-34$ Therefore, the required solutions are $\frac{-\text{b}\pm\sqrt{\text{D}}}{2\text{a}}=\frac{-(-2)\pm\sqrt{-34}}{2\times\sqrt{3}}=\frac{\sqrt{2}\pm\sqrt{34}\text{i}}{2\sqrt{3}}$ $[\sqrt{-1}=\text{i}]$
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