Question

The graph shows the system of equations that can be used to solve x^3+x^2=x-1.Which statement describes the roots of this equation?

Answer 1

Answer:

Equation has 1 real root and 2 complex roots.

Step-by-step explanation:

Given : $x^{3} +x^{2}$ =  $x -1$.

To find : Which statement describes the roots of this equation.

Solution : We have $x^{3} +x^{2}$ =  $x -1$.

We can write it as  $x^{3} +x^{2} - x -1$.

Graphs of both these functions shows one common point, this means that the equation $x^{3} +x^{2}$ =  $x -1$ 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.

Answer 2

Answer:

Equation has one real root and two complex roots.

Step-by-step explanation:

The equation $x^3+x^2=x-1$ consists of two parts. The left side of this equation can be represented by the function $y=x^3+x^2$ and the right side can be represented by the function $y=x-1.$ Graphs of both these functions are shown in the attached diagram.

These graphs have one common point, this means that the equation $x^3+x^2=x-1$ 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.