DeadShot
  • DeadShot
Which of the following is a polynomial with roots - square root of 5, square root of 5, and -3 ? x3 - 2x2 - 3x + 6, x3 + 2x2 - 3x - 6, x3 - 3x2 - 5x + 15, or x3 + 3x2 - 5x - 15?
Algebra
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
If you have roots of: a, b, and c your polynomial has the form: (x - a)(x - b)(x - c) = 0 Substitute a, b, and c for the given roots and multiply the expression out on the left side.
DeadShot
  • DeadShot
x^3 -2.25x^2+2.25x^2-3x2-2.25x+2.25x-3x-15
DeadShot
  • DeadShot
simplified, it's x^3-3x^2-3x-15, right?

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anonymous
  • anonymous
You wouldn't even have to ask that last question because you have 4 choices and this choice is not even listed among them. Here's a hint on how to expand that expression I gave you: (x - a)(x - b)(x - c) = 0 [(x - a)(x - b)](x - c) = 0 [x^2 - (a + b)x + ab](x - c) = 0 [x^2 - (a + b)x + ab]x - [x^2 - (a + b)x + ab]c = 0
DeadShot
  • DeadShot
[x^2-(-2.25+2.25)x + (-2.25)*2.25]x-[x^2-(-2.25+2.25)x + (-2.25)*2.25]-3=0
anonymous
  • anonymous
Where are you getting +-2.25 from? Neither has anything to do with sqrt(5).
DeadShot
  • DeadShot
sqrt(5) is approx 2.25
anonymous
  • anonymous
You don't want to be working with approximations here.
DeadShot
  • DeadShot
ok
DeadShot
  • DeadShot
x^3 - 3x^2 - 5x + 15
anonymous
  • anonymous
I would suggest evaluating the following first: [x - sqrt(5)][x + sqrt(5)] That correspond to the leftmost factors. Get that down to a trinomial.
DeadShot
  • DeadShot
that would be x^2-5
DeadShot
  • DeadShot
(x^2-5) (x-3)=x^3 - 3x^2 - 5x + 15
DeadShot
  • DeadShot
right?
anonymous
  • anonymous
The third root is "-3", so you have: [x - (-3)] or (x + 3) for that third factor. I think that's where you having your trouble. When you subtract a negative, it's like adding a positive.
anonymous
  • anonymous
So, taking up from where you were writing: (x^2 - 5)(x + 3) = 0 And then expand that. You are very close to your answer now.
DeadShot
  • DeadShot
so, it's x^3+3x^2-5x-15?
anonymous
  • anonymous
Yes! Excellent! Just remember about subtracting negatives and you will be ok.
DeadShot
  • DeadShot
Okay, Thanks for the help!
anonymous
  • anonymous
You're welcome! Good luck to you in all of your studies and thx for the recognition! @DeadShot
DeadShot
  • DeadShot
No problem!
anonymous
  • anonymous
x3 + 3x2 - 5x - 15 is not the correct answer (just took the test)
anonymous
  • anonymous
I am not incorrect. I took and worked on the problem that you were referring to, and I got x3 + 3x2 - 5x - 15 wrong. I take FLVS, so perhaps it was the computer grading system that was incorrect. Besides, this is a graded lesson. It would be extremely mean of me to INTENTIONALLY say inaccurate information.
anonymous
  • anonymous
Well I am practically done with the class now lol...I am mostly working on the module 10. It's like trig based. ^.^ I have my eoc next week, so I have been mega working XDD

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