Question

Help with polynomials

Answer 1

@mathstudent55

Answer 2

I don't understand how to find it :/

Answer 3

I think you expand it and then use discriminant?

Answer 4

Can you explain the discriminant

Answer 5

the "roots" of a polynomial are the x values that make the polynomial zero.
here you have
\[ (x-4)^2 (x^2+4) = 0\]
or
\[ (x-4) (x-4) (x^2+4) = 0\]
as you can see, if x= 4 (twice, so it is a repeated root) you get zero
you would also get 0 if x^2+4=0
or \( x^2= -4 \)
take the square root of both sides and you get
\[ x= 2i \text{ or } x=-2i\]

the 4 roots are:
4,4,+2i, -2i

Answer 6

Statement I is true: you have two imaginary roots: 2i and -2i

II is false: you do have the real root 4

III is true: you have four complex roots, namely 4,4, 2i and -2i

statement III is a bit tricky, because we must recognize that pure real (like 4) and pure imaginary (like 2i) can both be categorized as complex.

Answer 7

I and III are true.