Answer:
[tex]x= \frac{3-3\sqrt{7}i }{4}[/tex] and [tex]x= \frac{3+3\sqrt{7}i }{4}[/tex]
Step-by-step explanation:
We have to solve the given equation - 2x² + 3x - 9 = 0
To solve the equation given above we have to factorize the left-hand side of the equation.
But it can not be factorized. So, use the Sridhar Achaya formula.
Therefore, [tex]x= \frac{-3 + \sqrt{3^{2}-4 \times (-2) \times (-9) } }{2\times (-2)}[/tex] and [tex]x= \frac{-3 -\sqrt{3^{2}-4 \times (-2) \times (-9) } }{2\times (-2)}[/tex]
So, [tex]x= \frac{3-3\sqrt{7}i }{4}[/tex] and [tex]x= \frac{3+3\sqrt{7}i }{4}[/tex] {Where [tex]i=\sqrt{-1}[/tex]}
Therefore, the solutions are imaginary numbers. (Answer)
Note: The Sridhar Acharya Formula gives if ax² + bx + c = 0, then the roots of the equation are [tex]x = \frac{-b + \sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]x = \frac{-b - \sqrt{b^{2}-4ac } }{2a}[/tex].
