Question

The complex number 5+2i is a zero of a rational function. The graph of the function also has local maxima at (-1,0),(2,0) and (8,0). What is the least possible degree of the function

Answer 1

for a graph to have three local maxima

if you notice that graphs maxima and minima are 1 less that its degree

x²  has one turn or minima, it looks like ∪

x^ 3 has 2 turns

so to have three maxima its likely a x^4 or 4 degree equation

Answer 2

The degrees of a rational function is the highest power of the function.

The least possible degree (d) of the function is: (d) 4

The given parameters are:

$\mathbf{Zero = 5 + 2i}$

$\mathbf{Maxima = (-1,0)(2,0)(8,0)}$

The number of local maxima is 3

i.e.

$\mathbf{n = 3}$

So, the least possible degree (d) of the function is:

$\mathbf{d = n + 1}$

Substitute 3 for n

$\mathbf{d = 3 + 1}$

$\mathbf{d = 4}$

Hence, the least possible degree (d) of the function is: (d) 4

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