Equation roots Watch

Twiglet
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#1
Report Thread starter 12 years ago
#1
Im gonna cry... Im sure this is so easy but my brain just wont work it out at all maths and chocolate just dont mix...

show that x^3 -12x -7.2=0 has one positive and 2 negative roots.

See, simple :confused:
xxx
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Loz2402
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#2
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(Original post by franks)
Im gonna cry... Im sure this is so easy but my brain just wont work it out at all maths and chocolate just dont mix...

show that x^3 -12x -7.2=0 has one positive and 2 negative roots.

See, simple :confused:
xxx
ok here is my guess (not likely thats its right, but i'll say anyway!)

because there is no x^2, has it got to be similar to the difference of 2 squares. (...)(x-a)(x+a). this would give an answer (x^2-a) x another bracket. the third bracket would have to be postive to get the final answer with the two negative signs in.

so we have (x+a)(x-a)(x+b), which is +/- a, - b (2 neg, 1 pos)

any truth in that at all? :confused: lol
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Christophicus
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#3
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(Original post by franks)
Im gonna cry... Im sure this is so easy but my brain just wont work it out at all maths and chocolate just dont mix...

show that x^3 -12x -7.2=0 has one positive and 2 negative roots.

See, simple :confused:
xxx
x = -5, f(x) = -72.2
x = -4, f(x) = -23.2
x = -3, f(x) = 1.8
x = -2, f(x) = 8.8
x = -1, f(x) = 3.8
x = 0, f(x) = -7.2
x = 1, f(x) = -18.2
x = 2, f(x) = -23.2
x = 3, f(x) = -16.2
x = 4, f(x) = 8.8
x = 5, f(x) = 57.8

Change of sign in the intervals (-4,-3), (-1,0) and (3,4)
Hence two negative roots, and one positive.

f'(x) = 3x^2 - 12
So for x<-4, f'(x)>0, so curve doesn't meet x-axis again.
and for x>4 f'(x)>0, so curve doesn't meet x-axis again.
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Twiglet
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Report Thread starter 12 years ago
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x = -5, f(x) = -72.2
x = -4, f(x) = -23.2
x = -3, f(x) = 1.8
x = -2, f(x) = 8.8
x = -1, f(x) = 3.8
x = 0, f(x) = -7.2
x = 1, f(x) = -18.2
x = 2, f(x) = -23.2
x = 3, f(x) = -16.2
x = 4, f(x) = 8.8
x = 5, f(x) = 57.8
thanks, is there any other way of doing it apart from this though - as its seems a bit hit and miss which values to do f(x) between, hmm neat method tho!
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Malik
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If its C3 then widowmakers itteration method seems to be best way to go.
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Twiglet
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#6
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If its C3 then widowmakers itteration method seems to be best way to go
No its FP1...
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