Quadratic Watch

String.
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#1
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#1
What is the link between solving

2x^2 - 10x +5 =0

and


ln2(x^2) - ln10(x) + ln5=0


The first one is easy to solve and the second one takes ages, but I can see the link in the numbers I justdon't know how it works when solving :/
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Hasufel
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the linkage is that if you have this particular quadratic, and take the natural log of each successive term
in ax^{2}+bx+c=0, you then end up with just ln(x)=0

(EDITED for mistakes)
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String.
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(Original post by Hasufel)
the linkage is that if you have this particular quadratic, and take the natural log of each successive term
in ax^{2}+bx+c=0, you then end up with just ln(x)=0

(EDITED for mistakes)
So is that basically telling me that one of the answers is x=1?
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Hasufel
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Nope. If there is to be a "link" between both equations, then they must have to be solved simultaneously. If someone has told you there is a link, then it`s likely that`s what the link is. If so, then this can be solved using the Newton-Raphson iteration formula.

Try drawing the graphs, and you`ll see the points of intersection are somewhere in (0,1) and (4,5)

(hint: try the seed (the initial iteration point) for the left point as x=0.5, for the right point as x=4)

Other than that, there is no other "link" I can see.
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