Related

allroots

P2 =-945+744*x+739*x^...

allroots(P2);

Calculate

allroots-exp-solve

allroots(x^2 -1.99004...

solve(exp(-x/48000) =...

Calculate

dB(x):= 20*log10(x);

f_to_w(x):= 2*%pi*x;

Calculate

allroots-plot2d

U(x):=-x^4/4+x^3+4*x^...

plot2d([U(x),-5,14],[...

allroots(U(x)=25,x);

Calculate

allroots

allroots((578/100)*z-...

Calculate

allroots-create_list-diff-ev-exp-log-numer

p(x):=x*(x-1)*(x-2);

f(x):=p(x)*exp(-x*log...

t:diff(f(x),x)*exp(x*...

Calculate

allroots-create_list-diff-ev-exp-log-numer-ratsimp

/*p(x) is the polynom...

/* so f(x) should be ...

/* to calculate the l...

Calculate

dB(x):= 20*log10(x);

f_to_w(x):= 2*%pi*x;

Calculate

allroots

allroots(-x^4-x^3+6*x...

Calculate

allroots

allroots(-5,78*z^2+5,...

Calculate

allroots

Run Example
```(%i1)a:5;
(%o1)                                  5
(%i2) b:5;
(%o2)                                  5
(%i3) F:13;
(%o3)                                 13
(%i4) s:(a+b+c)/2;
c + 10
(%o4)                               ------
2
(%i5) g:F^2=s*(s-a)*(s-b)*(s-c);
c + 10     2  c + 10
(c + 10) (------ - 5)  (------ - c)
2             2
(%o5)              169 = -----------------------------------
2
(%i6) allroots(g);
(%o6) [c = 1.00000000000001 %i + 7.14142842854285,
c = 7.14142842854285 - 1.00000000000001 %i,
c = 0.99999999999999 %i - 7.14142842854285,
c = - 0.99999999999999 %i - 7.14142842854285]
(%i7) ```
Run Example
```U(x):=2*x^4+(x+1)*(2-x)-4;
4
(%o1)                 U(x) := 2 x  + (x + 1) (2 - x) - 4
(%i2) plot2d([3.5,U(x)],[x,-3,3],[y,-4,28]);
plotallroots(U(x)=3.5,x);
(%o3) [x = 1.310982762835513, x = - 1.460198402770752,
x = 1.196241579595596 %i + 0.07460781996762,
x = 0.07460781996762 - 1.196241579595596 %i]
(%i4) ```
Run Example
```load("log10");
(%o1)          /usr/share/maxima/5.21.1/share/contrib/log10.mac
(%i2) dB(x):= 20*log10(x);
(%o2)                        dB(x) := 20 log10(x)
(%i3) f_to_w(x):= 2*%pi*x;
(%o3)                        f_to_w(x) := 2 %pi x
(%i4) allroots(x^2 -1.99004745483398*x + 0.99007225036621);
(%o4) [x = 1.79564500253386E-4 %i + 0.99502372741699,
x = 0.99502372741699 - 1.79564500253386E-4 %i]
(%i5) allroots(x^2 -1.69065929318241*x + 0.73248077421585);
(%o5) [x = 0.13378551046297 %i + 0.84532964659121,
x = 0.84532964659121 - 0.13378551046297 %i]
(%i6) float(solve(exp(-x/48000) = 0.99502372741699,x)/(2*%pi));

rat: replaced -0.995023727417 by -8598/8641 = -0.995023724106
(%o6)               [0.1591549430919 x = 38.11085142032302]
(%i7) float(solve(exp(-x/48000) = 0.84532964659121,x)/(2*%pi));

rat: replaced -0.8453296465912 by -9783/11573 = -0.8453296465912
(%o7)               [0.1591549430919 x = 1283.644051295943]
(%i8) float(solve(exp(-x/48000) = 0.13378551046297,x)/(2*%pi));

rat: replaced -0.133785510463 by -1361/10173 = -0.1337855106655
(%o8)               [0.1591549430919 x = 15366.86120660835]
(%i9) H(s):= ((s^2)/(f_to_w(38.11085142032302)^2))/((s^2)/(f_to_w(38.11085142032302)^2) + s/(0.5*f_to_w(38.11085142032302)) + 1);
2
s
--------------------------
2
f_to_w (38.11085142032302)
(%o9) H(s) := --------------------------------------------------------------
2
s                              s
-------------------------- + ----------------------------- + 1
2                      0.5 f_to_w(38.11085142032302)
f_to_w (38.11085142032302)
(%i10) H2(s):= (1.52*(s^2)/(f_to_w(1283.644051295943)^2) + s/(0.13378551046297*f_to_w(1283.644051295943)) + 1)/((s^2)/(f_to_w(1283.644051295943)^2) + s/(0.5*f_to_w(1283.644051295943)) + 1);
(%o10) H2(s) :=
2
1.52 s                                  s
-------------------------- + ------------------------------------------ + 1
2                      0.13378551046297 f_to_w(1283.644051295943)
f_to_w (1283.644051295943)
---------------------------------------------------------------------------
2
s                              s
-------------------------- + ----------------------------- + 1
2                      0.5 f_to_w(1283.644051295943)
f_to_w (1283.644051295943)
(%i11) plot2d([dB(cabs(H(%i*f_to_w(f)))),dB(cabs(H2(%i*f_to_w(f))))],[f,10,24000],[logx,true]);
plot```

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