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The given fact will relate all of these ideas to the multiplicity of the zero.
Fact
If x = r is a zero of the polynomial P (x) along with multiplicity k then,
1. If the value of k is odd then the x-intercept corresponding to x = r will cross the x-axis
2. If value to k is even then the x-intercept corresponding to x = r will just touch the x-axis and not cross it actually.
Furthermore, if k = 1 then the graph will flatten out at the point x = r .
At last, notice that as we consider x get large in both the +ve or -ve sense (that means at either end of the graph) then the graph will either increase with no bound or decrease without bound. It will always occur with every polynomial and we can employ the following test to find out just what will happen at the endpoints of the graph.
1. In real world optimisation problems there is often an accompanying constraint that must also be satisfied. These problems are typically solved using "Lagrange Multipliers", whic
how do you simplify an expression of 100
4f=48
a+1/2=1
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Use synthetic division to divide 5x 3 - x 2 + 6 by x - 4 . Solution Okay along with synthetic division we pretty much avoid all the x's and just work with the numbers in
Whereas we are on the subject of function evaluation we have to now talk about piecewise functions. Actually we've already seen an instance of a piecewise function even if we didn'
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