Question

An aid in obtaining the first zero or the firs f(x)=x^(4)-12x^(3)+38x^(2)+116x+65

Answer 1

Hi,

Explanation:

evident root is x=-1 since:

`f(-1)=(-1)^4-12*(-1)^3+38*(-1)^2+116*(-1)+65=1+12+38-116+65=0\\`

with a multiplicity of 2, the 2 others are complex (7 – 4.i and 7 + 4.i)

`f(x)=(x+1)^2*(x-(7- 4*i))(x-(7 + 4.i))=(x+1)^2*(x-7+4*i)*(x-7-4*i)`