Math

Can someone check my work for this quadratic equation? Thank you.
b^4 + 2b^2 - 24 = 0
b^4 + 2b^2 = 24
(b^2)^2 + 2b^2 = 24
b^2 + 2b = 24
....
b = -2 +(-) ( Radical 4 - 4 (1)(-24) ) / 2(1)
b = -2 +(-) (Radical 100) /2
b = - 2 +(-) 10 / 2
b = -1 +(-) 5
b1 = 4 b2= -6

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asked by Maia
  1. Someone said I got it right, but then the response got deleted. Does that mean my answer is incorrect?

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    posted by Maia
  2. a 4th order equation usually has 4 solutions

    b^4 + 2b^2 - 24 = 0 ... (b^2 + 6)(b^2 - 4) = 0

    b^2 + 6 = 0 ... b = ± i √6

    b^2 - 4 = 0 ... b = ± 2

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    posted by R_scott
  3. suppose you let x = b^2
    then your equation becomes
    x^2 + 2x - 24 = 0
    This factors nicely to
    (x + 6)(x - 4) = 0
    x = -6 or x = 4

    then b^2 = -6 or b^2 = 4

    let's handle the b^2 = 4
    clearly b = ± 2

    what about the b^2 = -6
    there is no solution in the set of real numbers, since squaring any number would make it positive.
    If you have studied complex numbers, then
    b = ± i√6 , were i is defined as √-1

    as to your solution, you could have done:
    (b^2 + 6)(b^2 - 4) = 0
    to get b^2 = -6 or b^2 = 4 , same as my result above.

    your step from
    (b^2)^2 + 2b^2 = 24
    to
    b^2 + 2b = 24
    makes no sense.

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    posted by Reiny

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