Question

Find the solution to 3x² + 12x + 6 = 0 using completing the square method.


No spam!!

No copied answers!! ​

Answer 1

Answer:

-2 -$\sqrt{2\\}$  and  -2+$\sqrt{2}$  are solutions of the given quadratic equation

Step-by-step explanation:

Pls see attachment

Hope it helps!!

Pls mark as brainliest

Answer 2

$\large\underline{\sf{Solution-}}$

Given quadratic equation is

$\rm :\longmapsto\: {3x}^{2} + 12x + 6 = 0$

On dividing whole equation by 3, we get

$\rm :\longmapsto\: {x}^{2} + 4x + 2 = 0$

Now, add and subtract the square of half the coefficient of x, i.e add and subtract 4, we get

$\rm :\longmapsto\: {x}^{2} + 4x + 4 - 4 + 2 = 0$

$\rm :\longmapsto\: ({x}^{2} + 4x + 4) - 2 = 0$

$\rm :\longmapsto\: {(x + 2)}^{2} = 2$

$\rm :\longmapsto\:x + 2 = \: \pm \: \sqrt{2}$

$\rm :\longmapsto\:x + 2 = \: \pm \: \sqrt{2}$

$\rm :\longmapsto\:x = \: - 2 \: \pm \: \sqrt{2}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Additional Information

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac