Answer:
Roots of equation: [tex](-\sqrt{3}+3) (0) (-2) (-\sqrt{3}-3 )[/tex]
Integral roots : -2,0
Step-by-step explanation:
We have given that equation is [tex]x^4-4x^3 -6x^2+12x[/tex]
now, we solve the equation to find roots
[tex]x^4-4x^3 -6x^2+12x=0[/tex]
⇒[tex] (x) (x+2) (x^2-6x+6)[/tex]
we divide [tex]x^4-4x^3 -6x^2+12x[/tex] by [tex](x^2-6x+6)[/tex]
⇒[tex]-(-x+\sqrt{3}+3) (x+\sqrt{3}-3 ) (x) (x+2)[/tex]
we can clearly see the two roots through attached graph
From least to greatest : [tex](x+2) (x) -(-x+\sqrt{3}+3) (x+\sqrt{3}-3 )[/tex]
Roots of equation: [tex](-\sqrt{3}+3) (0) (-2) (-\sqrt{3}-3 )[/tex]
Integral roots : -2,0
