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anonymous

  • 5 years ago

|2x - 1| = x2

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  1. anonymous
    • 5 years ago
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    use the quadratic. Do you know what to do know?

  2. anonymous
    • 5 years ago
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    nope please explain

  3. anonymous
    • 5 years ago
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    Why do you use the quadratic for? Do you know why you have to use it now?

  4. anonymous
    • 5 years ago
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    no

  5. anonymous
    • 5 years ago
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    Actually no im wrong theres an absolute value.

  6. anonymous
    • 5 years ago
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    LOL

  7. anonymous
    • 5 years ago
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    Going from the definition, you can square both sides again (I'm skipping the sqrt of (2x-1)^2 bit) to get,\[(2x-1)^2=x^4\]You need to solve this equation. When you expand, you'll find,\[x^4-4x^2+4x-1=0\]The rational roots theorem says that if this polynomial is to have a rational root, it should be of the form +/- 1 (in this case). Substituting x=1 shows that it is indeed a root of the polynomial. So we may factor it out. Also, if you take the derivative of the polynomial, you'll find that x=1 is a root of the derivative also. This means x=1 is a double root of your quartic polynomial and you may factor out (x-1)^2. doing this yields\[x^4-4x^2+4x-1=(x-1)^2(x^2+2x-1)\]Setting this to zero leads you to conclude,\[x=1\]is a root (known) and \[x=-1 \pm \sqrt{2}\] from the quadratic.

  8. anonymous
    • 5 years ago
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    Thank you very much, gawww you are so knowledgeable in maths!

  9. anonymous
    • 5 years ago
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    You're welcome :)

  10. anonymous
    • 5 years ago
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    "Also, if you take the derivative of the polynomial, you'll find that x=1 is a root of the derivative also. This means x=1 is a double root of your quartic polynomial and you may factor out (x-1)^2. doing this yields"

  11. anonymous
    • 5 years ago
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    i'm confused about that part?

  12. anonymous
    • 5 years ago
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    One second...

  13. anonymous
    • 5 years ago
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    I was writing something up for that...just scratch it and note that the cubic you obtain when you factor (x-1) out of the quartic also has root x=1 by the rational root theorem. Then you can factor (x-1) from the cubic to obtain the quadratic.

  14. anonymous
    • 5 years ago
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    I didn't apply the derivative theorem for roots properly.

  15. anonymous
    • 5 years ago
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    oh i see thanks

  16. anonymous
    • 5 years ago
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    oops sorry for the triple post, my computer keeps lagging and when i do press it nothing comes up and then after like three tor two posts come up, LOL

  17. anonymous
    • 5 years ago
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    This website is weird, though.

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