Question

Hello people ~
factorise: x^2 + 3 √3 x + 6​

Answer 1

Using the quadratic formula,

∆=b²-4ac

∆=(3√3)²-4(1)(6)

∆=(9×3)-4(6)

∆=27-24

∆=3

`x1 = ( - b - √(3) )/(2a) = ( - 3 √(3) - √(3) )/(2) = \frac{ - 4 \sqrt[]{3} }{2}`

`x1 = - 2 √(3)`

Similarly,

`x 2 = ( - b + √(3) )/(2a) = \frac{ - 3 √(3) + \sqrt[]{3} }{2} = ( - 2 √(3) )/(2)`

`x2 = - √(3)`

Method 2:

x²-Sx+P=0

where S is the sum of the roots & P is the product of the roots.

x¹+x²= -3√3

x¹x²=6

Solving the system you get the same answers.

Your factored equation can be written in the form of:

(x-x¹)(x-x²)

(x+2√3)(x+√3)

Answer 2

`\\ \rm\rightarrowtail x^2+3√(3)x+6`

`\\ \rm\rightarrowtail x^2+√(3)x+2√(3)x+6`

`\\ \rm\rightarrowtail x(x+√(3))+2√(3)(x+√(3))`

`\\ \rm\rightarrowtail (x+2)(x+2√(3))`