## nickersia 2 years ago Medal to first who explains me this question :) Find the roots of the equation (comment).

1. nickersia

\[x ^{3}-x ^{2}-7x+3\]

2. shelbygt520

k whats the question

3. shelbygt520

ok do you want it factorized or what?

4. nickersia

That's problem, I'm not quite sure what should I do :s

5. shelbygt520

x^3+x^2-7x-3 One of the roots is x(1) = -3 After applying Polynomial remainder theorem you will have a second order equation x^2 - 2x - 1 = 0 a = 1 ; b = -2 ; c = -1 x(2,3) = (-b)(+/-)SqRoot{b^2 - 4 . a . c}/(2 a)= x(2,3) = (2)(+/-)SqRoot{4 - 4 . 1 . (-1)}/(2 . 1)= x(2,3) = (2)(+/-)SqRoot{4 + 4}/(2)= x(2,3) = 2 (+/-) SqRoot { 8 } / 2 = x(2,3) = 1 (+/-) SqRoot { 2 } ---> x(2) = 1 + SqRoot { 2 } ---> x(3) = 1 - SqRoot { 2 }

6. shelbygt520

u should do that but instead of doing minus you do the addition this was a mere example but close enough so that you would know what to do

7. nickersia

I understand second part perfectly that's not problem :) can you just explain how did you get -3 as one of the roots? I'm bit confused

8. shelbygt520

I just replaced +3 with -3 in this example

9. shelbygt520

so in your case the root would be +3

10. nickersia

Why is that?

11. shelbygt520

capish? :)