Question

What is the multiplicity of each of the roots of this graph?2

Answer 1

SOLUTIONS

What is the multiplicity of each of the roots of this graph?

`f(x)=2x^4+12x^3+16x^2-12x-18`

Factorise f(x) by the options

(a) According to the option we have -3 is a root of so x+3 is a factor

`(2x^4+12x^3+16x^2-12x-18)/(x+3)=2x^3+6x^2-2x-6`

(b) 1 is a root too so x - 1 is a factor

`(2x^3+6x^2-2x-6)/(x-1)=2x^2+8x+6`

`\begin{gathered} 2x^2+8x+6=2(x+3)(x+1) \\ f(x)=2(x+3)^2(x+1)(x-1) \end{gathered}`

Therefore the correct answer = Option A