Question

How many solutions does this system of equations have y=2x+5Y=x^3+4x^2+x+2

Answer 1

D. 3 solutions

Step-by-step explanation:

Given:

`\begin{gathered} y=2x+5 \\ \\ y=x^3+4x^2+x+2 \end{gathered}`

To find:

The number of solutions this system has

Let's equate the two equations and solve for x;

`\begin{gathered} 2x+5=x^3+4x^2+x+2 \\ \\ x^3+4x^2-2x+x+2-5=0 \\ \\ x^3+4x^2-x-3=0 \end{gathered}`

Since the highest power of x is 3, therefore, the system of equations will have 3 solutions