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Solve the quartic equation

2𝑥4 + 14𝑥3 + 6𝑥2 + 14𝑥 + 2 = 0

 Oct 25, 2018
 #1
avatar+103049 
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2𝑥4 + 14𝑥3 + 6𝑥2 + 14𝑥 + 2 = 0

 

This has an irreducible factorization.....there is an algebraic method for solving a quartic...but....it's EXTREMELY messy  !!!

 

We  can give approximate solutions with a  graph :   https://www.desmos.com/calculator/o4ek4yiqx4

 

There are only two real  roots  x ≈ -6.705   ans  x ≈ -0.149

 

The non-real roots are   x ≈ -0.07295 + 0.99734 i     and   x ≈ -0.07295 - 0.99734 i

 

[ The non-real roots were calculated using  Wolfram Alpha  ] :  https://www.wolframalpha.com/input/?i=2x%5E4+%2B+14x%5E3+%2B+6x%5E2+%2B+14x+%2B+2++%3D+0

 

cool cool cool

 Oct 25, 2018

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