Homework Help: calc

Posted by t on Tuesday, September 27, 2011 at 3:24pm.

A basic fact of algebra states that c is a root of a polynomial f(x) if and only if f(x) = (x-c)g(x) for some polynomial g(x). We say that c is a multiple root if f(x) = [(x-c)^2](h(x)) where h(x) is a polynomial.

Show that c is a multiple root of f(x) if and only if c is a root of both f(x) and f'(x)

calc - Steve, Tuesday, September 27, 2011 at 3:44pm
only if:
f(x) = (x-c)^2 h(x)
f'(x) = 2(x-c) h(x) + (x-c)^2 * h'(x)
= (x-c) * (2h + (x-c)*h^2)

This should get you going. The "if" logic kind of works backwards from here.

Answer this Question

Related Questions

algebra - What is the basic principle that can be used to simplify a polynomial...
Algebra - 2. What is the basic principle that can be used to simplify a ...
math - find a polynomial with integer coefficients such that square root of 3 + ...
math - find a polynomial with integer coefficients such that square root of 3 + ...
Calc - Find the functions a) f o g, b) g o f, c) f o f, d) g o g, and their ...
pre calc - The Identity Function The Squaring Function The Cubing Function The ...
College Algebra - I need some help with a handful of questions. I need to see ...
College Algebra - I need some help with a handful of questions. I need to see ...
College Algebra help please - I need some help with a handful of questions. I ...
Algebra 2 - Given that the polynomial has the given root, find all roots of the ...

For Further Reading

First Name:
School Subject:
Answer: