## mmbuckaroos Group Title Determine all of the roots of the given equation: x^3-2x^2-3x+10=0 2 years ago 2 years ago

1. shelovespiano Group Title

Complex, too? @mmbuckaroos?

2. shelovespiano Group Title

x=-2 x=2-i x=2+i

3. mmbuckaroos Group Title

Could you explaint o me how you got those so I can try my other problems please?

4. shelovespiano Group Title

Sorry, I'm a little low on time... if you bump your question, i'm sure someone else can help you. sorry!

5. mmbuckaroos Group Title

ok thanks

6. Mertsj Group Title

The possible rational roots are the factors of the constant term which is 10 divided by the factors of the coefficient of the term with the highest exponent which is the x^3 term. It's coefficient is 1. So the possible rational roots are: $\frac{\pm10}{1}, \frac{\pm5}{1}, \pm\frac{2}{1}, \frac{\pm1}{1}$

7. Mertsj Group Title

Use synthetic division to see if any of those are actually roots.

8. Mertsj Group Title

Since we have reason to believe that -2 is a root, let's try it.

9. Mertsj Group Title

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10. Mertsj Group Title

So we see that -2 is a root and now we must solve the quadratic equation x^2-4x+5=0 to find the other roots.

11. mmbuckaroos Group Title

ok this is the part that confuses me this division. My book here makes it so confusing

12. mmbuckaroos Group Title

like where do you get all of those numbers from? Sorry I just don't get this at all.

13. Mertsj Group Title

|dw:1335664387666:dw|

14. Mertsj Group Title

So you need help with synthetic division?

15. Mertsj Group Title

Do you understand the part about the possible rational roots?

16. mmbuckaroos Group Title

I actually think I figured out what you did to get those numbers now so nvm on that ? I understand the possible rational roots

17. Mertsj Group Title

So you need help with the synthetic division process?

18. mmbuckaroos Group Title

do i have to do the synthetic division for every possible rational root?

19. Mertsj Group Title

No. Just until you find one where the remainder is 0. That indicates that you have found a factor. Then you can start working on the quotient to find more roots.

20. mmbuckaroos Group Title

so it is a rootif it comes out equaling zero. ok so now that im following you we can keep going sorry about that

21. Mertsj Group Title

|dw:1335664711981:dw|

22. Mertsj Group Title

So since the second factor is a quadratic and it won't factor, we just plug it into the formula to find the roots.

23. Mertsj Group Title

Do you have another problem? Perhaps if we start another one from scratch, it will help you understand. I can guide you.

24. mmbuckaroos Group Title

yes one sec sorry

25. mmbuckaroos Group Title

x^3-x^2-4x-6=0

26. Mertsj Group Title

Can you list the possible rational roots?

27. Mertsj Group Title

It is so hard to help someone who won't respond.

28. mmbuckaroos Group Title

Sorry my computer shut down. Ok: +/-1, +/-1/6 ?

29. shelovespiano Group Title

He's not online anymore.... btw. I don't think I can help you, though, sorry:/ bump your question i guess?

30. mmbuckaroos Group Title

It's alright. I think I got it figured out. Feel bad I left him hanging there darn computer for some reason it doesn't ever like this site