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what would the roots be for the equation x*x*x-3*x*x+12x-10

 Mar 3, 2016
 #1
avatar+130491 
0

x^3 - 3x^x2 +12x - 10  = 0

 

1 is a root

 

Using synthetic division, we can find the other two roots

 

1     1    - 3     12     -10

                1     -2      10

       1      -2    10        0

 

The remaining polynomial is

 

x^2 - 2x  + 10       this has no real roots

 

The other two roots are:

 

1- 3i    and   1 + 3i

 

 

cool cool cool

 Mar 3, 2016
 #2
avatar+26397 
0

what would the roots be for the equation x*x*x-3*x*x+12x-10

 

x33x2+12x10=01331212110=0x1=1

 

If we have x1, then we can calcutate x2 and x3

x2=u+vix3=uvi

 

We can calculate u and v

ax3+bx2+cx+d=0u=12(x1+ba)v=(dax1+u2)i

 

x33x2+12x10=0ax3+bx2+cx+d=0a=1b=3c=12d=10x1=1u=12(1+31)=12(13)=12(2)u=1v=1011+12i=101+1i=10+1i=9i=9ii=3i2i2=1=3(1)v=3

 

x2=u+vix2=13ix3=uvix3=1(3)ix3=1+3i

 

laugh

 Mar 4, 2016

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