Question

Solve +3x - 9 = 0" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$x= \frac{3-3\sqrt{7}i }{4}$ and $x= \frac{3+3\sqrt{7}i }{4}$

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, $x= \frac{-3 + \sqrt{3^{2}-4 \times (-2) \times (-9) } }{2\times (-2)}$ and $x= \frac{-3 -\sqrt{3^{2}-4 \times (-2) \times (-9) } }{2\times (-2)}$

So,  $x= \frac{3-3\sqrt{7}i }{4}$ and $x= \frac{3+3\sqrt{7}i }{4}$ {Where $i=\sqrt{-1}$}

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 $x = \frac{-b + \sqrt{b^{2}-4ac } }{2a}$ and $x = \frac{-b - \sqrt{b^{2}-4ac } }{2a}$.