Sketch a graph of a function with the following properties:

Question

degree=5, positive lead coefficient, real zeros= 4 and -3(with multiplicity of 2)

 

I know there can be various answers for drawing this graph since you can't find out the polynomial function from the information given, but my teacher says I have to make up where the imaginary numbers would be.

Answer 1

If f(x) has real coefficients, then complex roots occur in conjugate pairs.  So, you could choose i and -i as two of the roots, for example.

 

If c is a root, then x - c is a factor.

 

So, an example of a polynomial function with the given properties would be:

 

f(x) = (x - 4)(x + 3)²(x - i)(x + i)