Thread: Finding roots of polynomial and zeros of multiplicity, is this correct?

Find roots of following polynomial and find zeroes of multiplicity.

f(x) = 4x^5 + 12x^4 + 9x^3

I got:
f(x) = 4x^5 + 12x^4 + 9x^3 = 0
x^3(4x^2 + 12x + 9) = 0
x^3(2x + 3)(2x + 3) = 0


x=0 OR x= -3/2
Because (2x+3) occurs two times, the multiplicity of -3/2 is 2 and the multiplicity of 0 is 1

Is it correct? Does it fully answer the question?

Originally Posted by mwok

Find roots of following polynomial and find zeroes of multiplicity.

f(x) = 4x^5 + 12x^4 + 9x^3

I got:
f(x) = 4x^5 + 12x^4 + 9x^3 = 0
x^3(4x^2 + 12x + 9) = 0
x^3(2x + 3)(2x + 3) = 0


x=0 OR x= -3/2
Because (2x+3) occurs two times, the multiplicity of -3/2 is 2 and the multiplicity of 0 is 1

Is it correct? Does it fully answer the question?

I would think so. This is my understanding of roots with multiplicity:

If f(x) is a polynomial, and a is a root of f, then (x - a) is a factor of f(x).
If (x - a) is a repeated factor, that is (x - a)^k is a factor of f(x), then a is a root with multiplicity k.