polynomial equation.

[stuart clark]

calculate value of \(\displaystyle x\) in \(\displaystyle (x+1)(x+2)(x+3)(x+4) = 120x^2\)

 

[galactus]

Subtract 120x^2 from both sides and rewrite as:

\(\displaystyle x^{4}+10x^{3}-85x^{2}+50x+24=(x-1)(x^{3}+11x^{2}-74x-24)=0\)

One root is easy to see now. Solve the remaining cubic and that's it.

All the roots are real, but not 'nice'.

 

[stuart clark]

Thanks for your reply. can you have any idea how can I solve cubic equation....

Thanks.

 

[Deleted member 4993]

Thanks for your reply. can you have any idea how can I solve cubic equation....

Thanks.

Like Galactus said those are not nice numbers. Using Newton-Raphson method,

x[sub:2tuh209g]1[/sub:2tuh209g] = -1.56348392502773E+01

x[sub:2tuh209g]2[/sub:2tuh209g] = -3.10405918921757E-01

x[sub:2tuh209g]3[/sub:2tuh209g] = 4.94524516919906E+00