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Explain the difference between a polynomial equation [eg. (x+1)(x-2)(x-4)=0] and a polynomial inequality [eg. (x+1) (x-2) (x-4) < 0]. What is the inequalityasking us to solve? Explain by graphing the function.

User Gota
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Answer:

Step-by-step explanation:

Here,we want to get the difference between a polynomial equation and a polynomial inequality

While a polynomial equation with respect to the given example looks for the value of the variable x equal to the value on the right hand side, a polynomial inequality on the other hand looks for the value of the variable x at which we have it related to the value on the right based on certain inequality symbols which in this case is less than. Thus, we are looking for the values of x which will make the given polynomial less than zero

The inequality is simply asking us to given the values of x in the polynomial which when susbtituted into it will make it less than zero

We have the plot of the two as follows:

The graph with the shaded part represents the one with the inequality. It is the region within which the solution to the inequality exists. It is the region within which we can find an answer or a value of x that would work for the polynomial inequality

For the first one however, the solution lies at the points where we have the graoh crossing the horizontal axis. The horizontal axis is touched at three points and that shows that there are three solutions only to the polynomial equation

However, for the polynomial inequality, there is a region which is shaded that indicates there are several solutions

Explain the difference between a polynomial equation [eg. (x+1)(x-2)(x-4)=0] and a-example-1
Explain the difference between a polynomial equation [eg. (x+1)(x-2)(x-4)=0] and a-example-2
User Naddy
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