What are polynomial zeros? (3/5)

What is a zero of polynomials?
If you prefer to watch, then head over to youtube.

We need them only because we often use polynomials in our modelling of physical and other situations! The zero is very useful because it helps find the root. So, why find the root?

Well, let’s say that we know we have the problem,

So, what can x be?

The question becomes much more simple if we reduce one side to zero making it .

Now, we can plug it in to the quadratic formula and find x.

Of course, you may say that this only applies to quadratics. However, given any polynomial, if you make it equal to zero, it becomes much easier to find the roots.

So, to answer your question, we don’t actually need the zeros, however they are really, really convenient!

If we take the following factorized polynomial:

P1(x) = (x-1)(x-2)(x-3)

Well, then any value of x where the above equation = “zero”.

So any time any of the above 3 expressions are zero, then naturally the product of all 3, will also be zero.

After factoring, this becomes easy enough to deduce and as we can see that when x is either 1, 2 or 3, the result of P1(x) will be zero.

Lets take another example that we can graph.

We can see from above, that our our points where each of the 3 terms will be zero, will be when x = [-2, -3/2, 2]. When we plot this polynomial, it is also evident in the graph.

I trust that clears up zero’s and these can now be seen in the next article when we discuss the multiplicity of a polynomial.

Ready for the next article?

https://shaun-enslin.medium.com/multiplicity-in-polynomials-3-3-55dc7e0a51fb