Question

find the roots of quadratic equation 3x^2 - 2root6x +2 =0

Answer 1

Step-by-step explanation:

The equation:

$3 {x}^{2} - 2 \sqrt{6} x + 2 = 0$

Let's break it,

You can see it's based on a+b whole squared relation

but it's not reliable method for all the quadratic equation cause oh! ofcourse not all of them are going to be a perfect square.

So I'm gonna use midterm split method:

$3 {x}^{2} - \sqrt{6} x - \sqrt{6}x + 2 = 0 \\ \sqrt{3} x( \sqrt{3} x - \sqrt{2} ) - \sqrt{2} ( \sqrt{3} x - \sqrt{2} ) = 0 \\ ( \sqrt{3} x - \sqrt{2} )( \sqrt{3} x - \sqrt{2} ) = 0$

Let's solve it furthur,

$\sqrt{3} x - \sqrt{2 } = 0 \\ \sqrt{3} x = \sqrt{2} \\ x = \sqrt{ \frac{2}{3} }$

And you got your root.