Answer:
Equation has one real root and two complex roots.
Step-by-step explanation:
The equation [tex]x^3+x^2=x-1[/tex] consists of two parts. The left side of this equation can be represented by the function [tex]y=x^3+x^2[/tex] and the right side can be represented by the function [tex]y=x-1.[/tex] Graphs of both these functions are shown in the attached diagram.
These graphs have one common point, this means that the equation [tex]x^3+x^2=x-1[/tex] has one real solution (approximately, x≈-1.839).
Given equation is cubic, then this equation has three roots. Since only one root is real, then two remaining roots are complex.
Answer:
Equation has 1 real root and 2 complex roots.
Step-by-step explanation:
Given : [tex]x^{3} +x^{2} [/tex] = [tex]x -1[/tex].
To find : Which statement describes the roots of this equation.
Solution : We have [tex]x^{3} +x^{2} [/tex] = [tex]x -1[/tex].
We can write it as [tex]x^{3} +x^{2} - x -1[/tex].
Graphs of both these functions shows one common point, this means that the equation [tex]x^{3} +x^{2} [/tex] = [tex]x -1[/tex] has one real solution (approximately, x≈-1.839).
But degree is 3 .
So, it has maximum 3 root.
Therefore, Equation has 1 real root and 2 complex roots.
