Solve the equation: `sqrt(3)x^2-sqrt(2)x+3sqrt(3)=" "0`

Answer

Solution



`{frac{1}{sqrt{6}}+frac{sqrt{34}}{2 sqrt{3}} i, frac{1}{sqrt{6}}-frac{sqrt{34}}{2 sqrt{3}} i}`

Explanation

The given equation is `\sqrt{3} x^{2}-\sqrt{2} x+3 \sqrt{3}=0`


This is of the form `a x^{2}+b x+c=0`, where `a=\sqrt{3}, b=-\sqrt{2}` and `c=3 \sqrt{3}`
$$ \therefore \quad\left(b^{2}-4 a c\right)=\left\{(-\sqrt{2})^{2}-4 \times \sqrt{3} \times 3 \sqrt{3}\right\}=(2-36)=-34<0 . $$
So, the given equation has complex roots.
These roots are given by
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