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

Equation has 1 real root and 2 complex roots.

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

Equation has one real root and two complex roots.

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.