Need help with solving an equation!

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doubledragon

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power of 3

What equation to solve ( power of 3) this ?

s^3+0.7s^2-0.05^s+1
 

Re: power of 3

you can use matlab

p=[1 0.7 -0.05 1];
r =roots(p)
 

Re: power of 3

ceaser said:
you can use matlab

p=[1 0.7 -0.05 1];
r =roots(p)
Click to expand...

Yes, but i need to solve by manually. any other method?
 

Re: power of 3

if i understand you well you want to factor this term.
if you really mean what you have written there then i can't help you; the reason is that its not a polynomial since "-0.05^s" (stop reading if this is the case)......but if you mean instead "-0.05*s^1" then this can be solved.
you could try doing this by taking the polynomial as (s-a)*(s-b)*(s-c) calculate and compare coefficients; you get a system of nonlinear equations;
but there is also an algorithm for solving cubic equations; its not so short as in quadratic case but it works; try this:
https://mathworld.wolfram.com/CubicFormula.html
 

Re: power of 3

if we have eqution like this

x^3+a1x^2+a2x+a3=0
it has three roots (r1,r2,r3)

(x-r1)(x-r2)(x-r3)

r1+r2+r3=-a1
r1r2+r2r3+r1r3=a2
r1r2r3=-a3

you can also solve any equation in third degree by cardan method
you can also solve any equation in fourth degree by ferary method
 

power of 3

for power 3 equation... mostly i try this two first (x-1) and (x+1)... then x-2 then x-3.... for integer roots...

then reduce the power 3 equation to quadratic equation... then it can b solved...

x = 1 and -1 mostly is the root....

sp
 

Re: power of 3

doubledragon,
As Ceaser suggests, use Cardan's method. This method is thoroughly described in the book "CRC Stanbdard Mathematical Tables" and in Burrington "Handbook of Mathematical Tables and Formulas". The mehtod for solving 4th order equations is also described. As you may know, 4th order is the highest order euation for which a closed form solution exists. Also, I'm sure that a Google search on Cardan will yield multiple hits.
Regards,
Kral
 

Re: power of 3

I will try the Cardan method to solve power of 3 and thanks to all of u
 

Re: power of 3

W can Use numerical method by try and error
 

Re: power of 3

num=[1 0.7 -0.05 1];
den=[1];
[z,p]=tf2zp(num,den)
zplane(num,den)


used extensively in DSP for Z-transform(matlab).it will give u zeroes+if any eq. has enominator,it will give as its poles.it will plot it also
 

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