Question

Determine consecutive values of x between which each real zero of each function is located. Then draw the graph.

$f\left(x\right)=x^4-4x^2+2$

Short answer

The consecutive values of x between which each real zero of the function is located are-2 and -1, -1 and 0, 0 and 1, 1 and 2.

Step-by-step solution

Step 1. Given Information.

Given to determine the consecutive values of x between which each real zero of the function $f\left(x\right)=x^4-4x^2+2$ is located. Then the graph needs to be drawn.

Step 2. Explanation.

The real zero of a function lies where the value of the function changes from positive to negative or negative to positive.

So, making a table of values of the function:

x	f(x)
-2	2
-1	-1
0	2
1	-1
2	2

Here the value of the function changes four times between -2 and -1, -1 and 0, 0 and 1, 1 and 2.

Graphing the function using the values in the table:

Step 3. Conclusion.

Hence the consecutive values of x between which each real zero of the function is located are -2 and -1, -1 and 0, 0 and 1, 1 and 2.