Respuesta :

[tex]\\ \rm\rightarrowtail x^2+3\sqrt{3}x+6[/tex]

[tex]\\ \rm\rightarrowtail x^2+\sqrt{3}x+2\sqrt{3}x+6[/tex]

[tex]\\ \rm\rightarrowtail x(x+\sqrt{3})+2\sqrt{3}(x+\sqrt{3})[/tex]

[tex]\\ \rm\rightarrowtail (x+2)(x+2\sqrt{3})[/tex]

subtomex0

Using the quadratic formula,

∆=b²-4ac

∆=(3√3)²-4(1)(6)

∆=(9×3)-4(6)

∆=27-24

∆=3

[tex]x1 = \frac{ - b - \sqrt{3} }{2a} = \frac{ - 3 \sqrt{3} - \sqrt{3} }{2} = \frac{ - 4 \sqrt[]{3} }{2} [/tex]

[tex]x1 = - 2 \sqrt{3} [/tex]

Similarly,

[tex]x 2 = \frac{ - b + \sqrt{3} }{2a} = \frac{ - 3 \sqrt{3} + \sqrt[]{3} }{2} = \frac{ - 2 \sqrt{3} }{2} [/tex]

[tex]x2 = - \sqrt{3} [/tex]

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)

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