Question

Please do this with quadratic formula

Answer 1

Quadratic formula for equation
$ax ^{2} + bx + c = 0$
is given by:

$x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$

Given equation is
$3 {x}^{2} - 2 \sqrt{6} x + 2 = 0$
Plug in the values,

$x = \frac{2\sqrt{6} \pm \sqrt{(2\sqrt{6})^{2}-4×3×2}}{2×3}$

$x = \frac{\sqrt{6}}{3}$

The equation has two equal roots, namely
$\frac{ \sqrt{6} }{3}$

Answer 2

$\huge{\mathfrak{\red{\underline{\underline{Answer :-}}}}}$

$\large{\mathrm{\underline{\gray{Given :-}}}}$

Equation :- 3x² - 2√6x + 2

a = 3

b = 2√6

c = 2

$\large{\mathrm{\underline{\gray{To \: Find :-}}}}$

Roots by using quadratic formula

$\large{\mathrm{\underline{\gray{Solution :-}}}}$

[Distinct Method]

$\huge{\boxed{\boxed{\bf{D \: = \: b^{2} \: - \: 4ac}}}}$

___________________[Put Values]

D = (2√6)² - 4(3)(2)

D = 24 - 24

D = 0

✯ We know that when D is equal to zero. Then, equation has to real and equal roots

√D = 0

Quadratic Formula :-

$\huge{\bf{\boxed{\boxed{x \: = \: {\frac{-b \: ± \: {\sqrt{D}}}{2a}}}}}}$

______________[Put values]

x = -(-2√6) ± 0 / 2(3)

x = 2√6 + 0 / 6 = √6/3

x = 2√6 - 0 / 6 = √6/3

________________________

$\huge{\bf{\boxed{\boxed{x \: = \frac{\sqrt6}{3}}}}}$