I have the following polynomial: e^x - 3*x^2
I am trying to find real roots. I use solve.
(%i7) p: (%e)^x - 3*x^2;
x 2
(%o7) %e - 3 x
(%i8) p;
(%i14) solve(p,x);
x/2 x/2
%e %e
(%o14) [x = - -------, x = -------]
sqrt(3) sqrt(3)
(%i15) solve(p,x),numer;
`rat' replaced 0.33333333333333 by 1/3 = 0.33333333333333
`rat' replaced -0.5773502691896 by -2911/5042 = -0.5773502578342
`rat' replaced 1.0 by 1/1 = 1.0
`rat' replaced -2.449293598294706E-16 by -1/4082809838298842 = -2.449293598294706E-16
`rat' replaced 0.5 by 1/2 = 0.5
`rat' replaced -0.5773502578342 by -2911/5042 = -0.5773502578342
`rat' replaced 1.0 by 1/1 = 1.0
`rat' replaced -2.449293598294706E-16 by -1/4082809838298842 = -2.449293598294706E-16
`rat' replaced 3.4490250987489918E-18 by 1/289937002883137472 = 3.4490250987489918E-18
`rat' replaced 0.5 by 1/2 = 0.5
`rat' replaced 0.5 by 1/2 = 0.5
`rat' replaced 0.5 by 1/2 = 0.5
`rat' replaced -0.5773502691896 by -2911/5042 = -0.5773502578342
`rat' replaced -1.0 by -1/1 = -1.0
`rat' replaced 1.2246467991473532E-16 by 1/8165619676597685 = 1.2246467991473532E-16
`rat' replaced 0.5 by 1/2 = 0.5
`rat' replaced -0.5773502578342 by -2911/5042 = -0.5773502578342
`rat' replaced -1.0 by -1/1 = -1.0
`rat' replaced 1.2246467991473532E-16 by 1/8165619676597685 = 1.2246467991473532E-16
`rat' replaced -2.428890914611966E-20 by -1/41171054409405521920 = -2.428890914611966E-20
`rat' replaced 0.5 by 1/2 = 0.5
`rat' replaced 0.5 by 1/2 = 0.5
`rat' replaced 0.5 by 1/2 = 0.5
0.5 x
(%o15) [x = 2.4288909146119663E-20 (2911 %i - 23770118878575861035) %e ,
0.5 x
x = - 3.4490250987489918E-18 (41 %i - 167395203370252522) %e ]
So, I get two roots, which don't make sense to me. Using newton's method
I get approximations for 3 real roots below:
(%i17) load(newton1);
(%o17) /usr/share/maxima/5.13.0/share/numeric/newton1.mac
(%i21) newton(p,x,4,10^-5);
(%o21) 3.733079028654685
(%i22) newton(p,x,0,10^-5);
(%o22) - 0.45896227419484
(%i24) newton(p,x,2,10^-5);
(%o24) 0.91000757254889
Am I doing something wrong? Am I not supposed to use solve to find the
roots of this polynomial? Why do I get 2 roots instead of three? And 2
wrong ones?
I probably don't see something obvious. I am new to maxima. Just started
using it...
--
"When I was a kid I used to pray every night for a new bicycle. Then I
realised that the Lord doesn't work that way so I stole one and asked
Him to forgive me."
- Emo Philips.