How do you write a polynomial function given the real zeroes 1,-4, 5 and coefficient 1?
2 Answers
The simplest such polynomial is:
#f(x) = (x-1)(x+4)(x-5) = x^3-2x^2-19x+20#
Explanation:
Convert the zeros into linear factors to find:
#f(x) = (x-1)(x+4)(x-5) = x^3-2x^2-19x+20#
Any polynomial in
Begin from the factored form to find the desired polynomial to be
Explanation:
An easy way of generating a polynomial with a given set of zeros is to begin with the factored form. A polynomial
Using this, we can construct the desired polynomial as follows:
Note that we could multiply by a constant to give