Q1. - Algebra 2

Question

Explain the Location Principle in your own words.

Step-by-Step Solution

Answer

In own words: If $f$ is continuous such that $f\left(a\right)<0$ and $f\left(b\right)>0$. So $f\left(x\right)$ is going from a negative value to positive value continuously. So, it must be zero at least somewhere in the middle. 

When $f\left(x\right)$ is zero there we get a real zero. The number of times it cuts/touches the x-axis then we get a real zero.

Step 1. Given

Location principle.

Step 2. To determine

We have to explain location principle.

Step 3. Calculation

Location principle: Suppose $y=f\left(x\right)$ represents a polynomial function and a and b are two numbers such that $f\left(a\right)<0$ and $f\left(b\right)>0$. Then the function has at least one real zero between a and b.

 

In own words: If $f$ is continuous such that $f\left(a\right)<0$ and $f\left(b\right)>0$. So $f\left(x\right)$ is going from a negative value to positive value continuously. So, it must be zero at least somewhere in the middle. 

When $f\left(x\right)$ is zero there we get a real zero. The number of times it cuts/touches the x-axis then we get a real zero.