## anonymous 2 years ago Could someone walk me through this question and explain to me what happens. I have been working on it for 7 hours. I don't understand my prof and I might fail the class and I want to cry. Its solving a quadratic equation that had complex numbers

1. anonymous

$2x^2-ix-2+i=0$

2. anonymous

:/ Sorry... I can't help..

3. anonymous

:'(

4. anonymous

@jdoe0001

5. anonymous

tried using the quadratic formula yet?

6. anonymous

Phew! GO JDOE!

7. anonymous

I tried it, i solved it but i got the wrong answers. I tried it over and over again. I looked up videos, still wrong answer

8. anonymous

$$\large \begin{array}{llll} {\color{red}{ 2}}x^2&{\color{blue}{ -i}}x&{\color{green}{ -2+i}}=0\\ \uparrow &\ \uparrow &\quad \uparrow \\ {\color{red}{ a}}&\ {\color{blue}{ b}}&\quad {\color{green}{ c}} \end{array}\\ \quad \\ \bf x=\cfrac{i\pm\sqrt{i^2-4(2)(-2+i)}}{2(2)}\implies x=\cfrac{i\pm\sqrt{-1-8(-2+i)}}{2(2)}\\ \quad \\ x=\cfrac{i\pm\sqrt{-1+16-8i}}{2(2)}\implies x=\cfrac{i\pm\sqrt{15-8i}}{4}$$

9. anonymous

ok..got that

10. anonymous

well.. that's.... as far as I can see it going... what does your answer say?

11. anonymous

x=1 and x=-1+0.5i

12. anonymous

hmmm I don't see it simplifying ... to that

13. anonymous

:(

14. anonymous

|dw:1389574709566:dw|

15. anonymous
16. anonymous

how did u do that

17. anonymous

that is an algorithm

18. anonymous

19. anonymous

|dw:1389575164382:dw|

20. anonymous

wait...is this like synthetic division

21. anonymous

|dw:1389575421091:dw|

22. anonymous

this is the briot-ruffini algorithmm, i don't what is synthetic division

23. anonymous

so in my question the root is 2?

24. anonymous

no the root is one, the first coef in your polynomial is 2

25. anonymous

how do i know what the root is?

26. anonymous

one, was a easy root to see in that problem

27. anonymous

oh. so if it had all 4...then it will be 2?

28. anonymous

could u do it step by step and explain what you were doing at each step

29. anonymous

|dw:1389575930097:dw|