Question

roots of the equation 3x^2-2x+3 are

Answer 1

Answer:

$\frac{2+2\sqrt{2i} }{3} , \frac{2-2\sqrt{2i} }{3}$

Step-by-step explanation:

We have to find the roots of the given equation 3x^2-2x+3

∵ The given equation is quadratic , so there will be two values of  x.

The given equation is $3x^{2} - 2 \times x  + 3$

Now applying Sreedharacharyas rule to find the roots;

$D =  b^{2}  - 4 \times a \times c$

$D = 4- 4 \times3 \times3$

D = -32

So there will be two values of x

$x= \frac{-b + \sqrt{D} }{2 \times a}$  and  $x= \frac{-b - \sqrt{D} }{2 \times a}$

$x = \frac{ 4 + \sqrt{-32} }{6}$ and $x = \frac{ 4 - \sqrt{-32} }{6}$

∴   $x = \frac{ 2 + 2\sqrt{2i} }{3}$ and   $x = \frac{ 2 - 2\sqrt{2i} }{3}$