## DarkBlueChocobo one year ago Help with polynomials

1. DarkBlueChocobo

2. DarkBlueChocobo

@mathstudent55

3. DarkBlueChocobo

I don't understand how to find it :/

4. anonymous

I think you expand it and then use discriminant?

5. DarkBlueChocobo

Can you explain the discriminant

6. phi

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

7. phi

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.

8. ali2x2

I and III are true.