anonymous
  • anonymous
Determine all of the roots of the given equation: x^3-2x^2-3x+10=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Complex, too? @mmbuckaroos?
anonymous
  • anonymous
x=-2 x=2-i x=2+i
anonymous
  • anonymous
Could you explaint o me how you got those so I can try my other problems please?

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anonymous
  • anonymous
Sorry, I'm a little low on time... if you bump your question, i'm sure someone else can help you. sorry!
anonymous
  • anonymous
ok thanks
Mertsj
  • Mertsj
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: \[\frac{\pm10}{1}, \frac{\pm5}{1}, \pm\frac{2}{1}, \frac{\pm1}{1}\]
Mertsj
  • Mertsj
Use synthetic division to see if any of those are actually roots.
Mertsj
  • Mertsj
Since we have reason to believe that -2 is a root, let's try it.
Mertsj
  • Mertsj
|dw:1335664232988:dw|
Mertsj
  • Mertsj
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.
anonymous
  • anonymous
ok this is the part that confuses me this division. My book here makes it so confusing
anonymous
  • anonymous
like where do you get all of those numbers from? Sorry I just don't get this at all.
Mertsj
  • Mertsj
|dw:1335664387666:dw|
Mertsj
  • Mertsj
So you need help with synthetic division?
Mertsj
  • Mertsj
Do you understand the part about the possible rational roots?
anonymous
  • anonymous
I actually think I figured out what you did to get those numbers now so nvm on that ? I understand the possible rational roots
Mertsj
  • Mertsj
So you need help with the synthetic division process?
anonymous
  • anonymous
do i have to do the synthetic division for every possible rational root?
Mertsj
  • Mertsj
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.
anonymous
  • anonymous
so it is a rootif it comes out equaling zero. ok so now that im following you we can keep going sorry about that
Mertsj
  • Mertsj
|dw:1335664711981:dw|
Mertsj
  • Mertsj
So since the second factor is a quadratic and it won't factor, we just plug it into the formula to find the roots.
Mertsj
  • Mertsj
Do you have another problem? Perhaps if we start another one from scratch, it will help you understand. I can guide you.
anonymous
  • anonymous
yes one sec sorry
anonymous
  • anonymous
x^3-x^2-4x-6=0
Mertsj
  • Mertsj
Can you list the possible rational roots?
Mertsj
  • Mertsj
It is so hard to help someone who won't respond.
anonymous
  • anonymous
Sorry my computer shut down. Ok: +/-1, +/-1/6 ?
anonymous
  • anonymous
He's not online anymore.... btw. I don't think I can help you, though, sorry:/ bump your question i guess?
anonymous
  • anonymous
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

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