DeadShot 2 years ago 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?

1. tcarroll010

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.

x^3 -2.25x^2+2.25x^2-3x2-2.25x+2.25x-3x-15

simplified, it's x^3-3x^2-3x-15, right?

4. tcarroll010

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

[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

6. tcarroll010

Where are you getting +-2.25 from? Neither has anything to do with sqrt(5).

sqrt(5) is approx 2.25

8. tcarroll010

You don't want to be working with approximations here.

ok

x^3 - 3x^2 - 5x + 15

11. tcarroll010

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.

that would be x^2-5

(x^2-5) (x-3)=x^3 - 3x^2 - 5x + 15

right?

15. tcarroll010

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.

16. tcarroll010

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.

so, it's x^3+3x^2-5x-15?

18. tcarroll010

Yes! Excellent! Just remember about subtracting negatives and you will be ok.

Okay, Thanks for the help!

20. tcarroll010

You're welcome! Good luck to you in all of your studies and thx for the recognition! @DeadShot

No problem!

22. malice

x3 + 3x2 - 5x - 15 is not the correct answer (just took the test)

23. malice

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.

24. malice

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