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Which correctly describes the root of the following cubic equation? x^3-3x^2+4x-12=0

User Nahidf
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1 Answer

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Answer:

The equation has one real root and two complex roots.

Explanation:

The given equation is


x^3-3x^2+4x-12=0

The above equation is true form x=3, therefore (x-3) is a factor of above equation.

Use long division or synthetic division method to divide the equation by (x-3).


(x-3)(x^2+4)=0

Equate each factor equal to zero.


x-3=0


x=3

Therefore 3 is a real root of the equation.


x^2+4=0


x^2=-4


x=√(-4)


x=\pm 2i

2i and -2i are complex roots of the equation.

Therefore the equation has one real root and two complex roots.

User Silagy
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