Question

3x2-6x+2=0 using quadratic equation formula ​

Answer 1

Answer:

$\bold{\huge{\text{The equation has two equal roots; }\sqrt2/\sqrt3}}$

Step-by-step explanation:

$3 x^{2} -2\sqrt6x+2=0\\3 x^{2} -\sqrt6x-\sqrt6x+2=0\\\sqrt3 x^{2} \times\sqrt3 x^{2} -\sqrt3x\times\sqrt2x-\sqrt3x\times\sqrt2x+\sqrt2\times\sqrt2=0\\\sqrt3x(\sqrt3x-\sqrt2)-\sqrt2(\sqrt3x-\sqrt2)=0\\(\sqrt3x-\sqrt2)(\sqrt3x-\sqrt2)=0\\x=\sqrt2/\sqrt3\\\text{Therefore the equation has two equal roots; }\sqrt2/\sqrt3$

Answer 2

$\huge\mathcal{Extra\: Information }$

Solution of a quadratic equation by using quadratic formula : For the quadratic equation $a{x}^{2} + bx + c = 0 , its root are given by the quadratic formula , </p><p></p><p>[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a}$

$if \: {b}^{2} - 4ac > 0 \: or \: {b}^{2} - 4ac = 0$

Where ,

${b}^{2} - 4ac \: is \: called \: the \: discriminant \: of \: the \: equation \: .$

$\huge\mathcal{Solution}$

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

Here in this equation .....

a = 3

b = 6

c = 2

Now , by using quadratic equation ....

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

$x = - 6 + - \frac{ \sqrt{ {6}^{2} - 4.3.2} }{2.3}$

$x = - 6 + - \frac{ \sqrt{36 - 24} }{6}$

$x = - 6 + - \frac{ \sqrt{12} }{6}$

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

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

Hence ,

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

and

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