How do I write a polynomial of least degree?

Question

1. 4,5

2. 3,-5, 1

3. 3, 3, 1, 1, -2

4. 2i, 3, -3

5. 1-2i, 3

Answer 1

Undoubtedly the question, in full, should be "How do I write a polynomial of least degree, having the listed zeros (assuming that all coefficients and constants in the polynomial are Real numbers)?

 

Answer, in general, is (x-root₁)(x-root₂)... = p(x).  [I say "root" because these zeros are roots of the equation p(x)=0]

 

When a complex root is given, recall that these occur in conjugate pairs, i.e. if 1-2i is a zero then so is 1+2i. So in the case of problem 5, you will produce a degree 3 polynomial.

 

Whether you leave these in factored form or multiply them out is up to you since it was not stated that 'standard form' is required.