Find an effeciant way to deduce the roots of the equatioon

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To find the roots of the fourth-order equation x^4 + 5x^2 + 6 = 0, participants suggest using substitution methods to simplify the equation. Graphing the function is also mentioned as a potential approach to visualize the roots. Iterative methods are considered, though concerns arise about the need for a specific form of the equation to apply them effectively. The discussion highlights the importance of proper notation for exponents in mathematical expressions. Overall, substitution appears to be the most efficient method proposed for solving the equation.
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Homework Statement



Consider the fourth order equation x4 + 5x2 + 6 = 0.
(a) Suggest an efficient way to find all roots of this equation.
(b) List all the roots.


Homework Equations





The Attempt at a Solution



-I plotted the graph.
-I thought of iteration - Is that correct ? For that I have to change the form of the equation but then it is not given - Usually for iteration, they mention.
-I thought of first derivative but what use is it going to be ?
 
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Can you find a suitable substitution??

By the way, if you want to type an exponent such as x2. Then you can do this by

Code: 
[NOPARSE]x[SUP]2[/SUP][/NOPARSE]
 
Yes, I got it with substitution !

Thanks a lot ! And I will use the proper way for exponent next time.
 
engboysclub said:
Yes, I got it with substitution !

Thanks a lot ! And I will use the proper way for exponent next time.

Or: you can just write x^2 and x^4; these are also perfectly understandable.

RGV
 

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