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BrianaNicole19 Group Title

Connections help?? I totally forgot how to do this! :/ 2x^3 – 5x^2 – 3x + 2 = 2

  • one year ago
  • one year ago

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  1. JasonEay Group Title
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    X's possible solutions are -1/2, 0, and 3.

    • one year ago
  2. BrianaNicole19 Group Title
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    Howd you get that.?

    • one year ago
  3. whpalmer4 Group Title
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    I would start by subtracting 2 from each side, to give \[2x^3-5x^2-3x=0\] Now we start factoring: there's a common x in all 3 terms: \[x(2x^2-5x-3)=0\] so x = 0 is one solution

    • one year ago
  4. whpalmer4 Group Title
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    Now you can factor \[2x^2-5x-3\] or use the quadratic formula to get the other two.

    • one year ago
  5. saloniiigupta95 Group Title
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    Subtract 2 from both sides, you will be left with- \[2 x^3 - 5 x^2 -3x =0\] Now take x common from it, and factor the remaining...

    • one year ago
  6. whpalmer4 Group Title
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    To factor, we'll have something like (2x+a)(x+b) for appropriate values of a and b, giving: (2x+a)(x+b) = 2x^2 + ax + 2bx + ab = 2x^2 + (a+2b)x + ab To make that the same as 2x^2-5x-3, we need to find a and b such that ab = -3 and (a+2b)=-5. a moment of thought should tell you that a=1, b=-3 so our remaining terms factor to (2x+1)(x-3) and the whole thing is \[x(2x+1)(x-3)=0\] with solutions at x=0, x=-1/2, x=3

    • one year ago
  7. whpalmer4 Group Title
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    (the solutions simply being the values of x that make the product terms = 0)

    • one year ago
  8. BrianaNicole19 Group Title
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    Soo.. is the answer 0 or all of the above O.o

    • one year ago
  9. whpalmer4 Group Title
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    All 3 of those values will make the polynomial = 0. x=0: \[2(0)^3-5(0)^2-3(0) = 0\] x=3: \[2(3)^3-5(3)^2-3(3) = 54-45-9 = 0\] x=-1/2: check this one yourself :-)

    • one year ago
  10. whpalmer4 Group Title
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    In general, you'll have as many solutions as the power of the highest order term in the polynomial. We have an x^3, so there are 3 solutions. Some of them may be complex numbers, but in this case, they were all real numbers.

    • one year ago
  11. BrianaNicole19 Group Title
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    I remember now(: Thanks that helped a lot!

    • one year ago
  12. whpalmer4 Group Title
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    It's just like riding a bicycle, right? :-)

    • one year ago
  13. whpalmer4 Group Title
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    A bicycle that tries to grab your pants in the chain send you crashing to the ground! :-)

    • one year ago
  14. BrianaNicole19 Group Title
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    Except all that you have to remember is to pedal and keep balance.. Algebra you have to remember a lot more and youll never use it haha

    • one year ago
  15. BrianaNicole19 Group Title
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    Lol yes that is very true!

    • one year ago
  16. whpalmer4 Group Title
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    Well, I suppose it depends on what path you take through life, but I encounter algebra quite often — it just doesn't always say "ALGEBRA" in big red letters on the cover. Now, finding the roots of cubic polynomials might be something that you won't do very often, agreed...but doesn't it feel good to be able to look at something that so many people around you are likely to say "oh, that's hard, I can't do that" and think "I can do that!"?

    • one year ago
  17. whpalmer4 Group Title
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    Here's a secret: a lot of it is simply not believing that you can't do it! The math they teach before calculus really isn't that difficult; becoming proficient at it just requires the right explanation, and practice. Unfortunately, not every teacher can supply the right explanation for every student, and the practice takes time which some aren't willing to devote.

    • one year ago
  18. BrianaNicole19 Group Title
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    Yes! It is awesome knowing I can do something most older people cant even do! But, I don't think I'll be encountering any of this in the area I'm going into except for maybe the basics My last school the kids didn't even try to learn they just starred at it as if it were a foreign language and it could have been the simplest thing ever

    • one year ago
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