anonymous
  • anonymous
Solve: x^3-2x^2-5x+6=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Please help!
TuringTest
  • TuringTest
first thing I do in these situations is check if you get lucky and have +/-1 be a solution...
anonymous
  • anonymous
Answer: x= -2 , x= 1 and x = 3

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Mertsj
  • Mertsj
Did you try synthetic division?
anonymous
  • anonymous
No, I haven't tried synthetic division because I was unsure how to start it? Do I just pick number I think will work?
Mertsj
  • Mertsj
The factors of the constant term, which is 6, are +-1, +-2, +-3, +-6. Would you agree?
Mertsj
  • Mertsj
The coefficient of the x^3 term is 1. So the possible rational roots are the factors of the constant term divided by the factors of 1.
anonymous
  • anonymous
Yes that makes sense. Okay, so now I try all of those numbers?
Mertsj
  • Mertsj
\[\pm1, \pm2,\pm3, \pm 6\]
Mertsj
  • Mertsj
i usually start with the small ones.
Mertsj
  • Mertsj
|dw:1327802691317:dw|
Mertsj
  • Mertsj
Look at that. We stumbled onto one first thing. That means that one factor is (x-1) And the other factor is x^2-x-6 which can then be factored by the usual methods.
Mertsj
  • Mertsj
So we have: (x-1)(x^2-x-6)= (x-1)(x-3)(x+2)=0 So x=1, 3, or -2
anonymous
  • anonymous
I'm sorry, but could you explain how we got x^2-x-6? I understand how we found the first one but now I am rather lost
Mertsj
  • Mertsj
I will repost the synthetic drawing and then you will see.
Mertsj
  • Mertsj
|dw:1327802958637:dw|
Mertsj
  • Mertsj
It's the same as when you divide anything. Like 12 divided by 4 = 3 because 3 times 4 = 12
anonymous
  • anonymous
Okay thank you. I understand now. You are a life saver!
Mertsj
  • Mertsj
S= x^3-2x^2-5x+6 divided by x-1 = x^2-x-6 because (x-1)(x^2-x-6)=x^3-2x^2-5x+6
Mertsj
  • Mertsj
You are very welcome.

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