## Mimi_x3 4 years ago The polynomial P(x) = x^3 - 2x^2 + kx + 24 has roots a , b and γ (i) It is known that two of the roots are equal in magnitude but opposite in sign. Find the third root and hence find the value of k Can you please help .

1. oktalBlizzard

:@

2. Mimi_x3

:@ ?? why yu angry ? LOL

3. aredsani

3rd root is 2

4. oktalBlizzard

not angry

5. oktalBlizzard

6. Mimi_x3

how is 3rd root 2 ?

7. Mimi_x3

lols , having a bad day ? why ?

8. oktalBlizzard

I passed the entry test to uni, but apparently, I need to get minimum of 2 A levels to get into it. A levels take 2 years to get. I have 4 months.

9. Mimi_x3

ohh ok LOL

10. estudier

I got so far (for roots a,-a and c) 3a +c = 2 and a^2 c = 24 U get that?

11. Mimi_x3

yeah

12. Mimi_x3

w8 , what's c ?

13. estudier

I don't mean understand, I mean u calculated same?

14. estudier

I said for roots, a,-a and c

15. Mimi_x3

ohh lols , i dnt even know how to do it

16. estudier

There is similar (not same) formula like Vieta for cubic as for quadratic....

17. Mimi_x3

What's Vieta ?

18. estudier

Formulae for sum and product of roots of quadratic.

19. Mimi_x3

ohh that

20. jimmywhoaaw

Let a be the first root >0. Then b=-a Now since a cubic function with 3 real roots then must be of the form: (x-a)(x-b)(x-v)= x^3 - 2x^2 + kx + 24 But b=-a so LHS is (x-a)(x+a)(x-v)=(x^2-a^2)(x-v) Multiplying the left hand side out we get: =x^3-v*x^2-a^2*x+v*a^2=P(x) From this we see that v=2 which implies 24=2*a^2 then a^2=12 but -a^2*x=kx thus k=-12

21. Mimi_x3

thank you (: