Find an effeciant way to deduce the roots of the equatioon

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  • #1
engboysclub
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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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  • #2
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]
 
  • #3
Yes, I got it with substitution !

Thanks a lot ! And I will use the proper way for exponent next time.
 
  • #4
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
 

1. How can we find the roots of an equation efficiently?

To find the roots of an equation efficiently, we can use various methods such as the quadratic formula, factoring, or using numerical methods like Newton's method or the bisection method.

2. What is the most commonly used method to deduce the roots of an equation?

The most commonly used method to deduce the roots of an equation is the quadratic formula, especially for equations in the form of ax^2 + bx + c = 0.

3. Can we use the same method to find the roots of all types of equations?

No, the method used to find the roots of an equation depends on the type of equation. For example, the quadratic formula can be used for quadratic equations, but for higher order equations, we may have to use other methods such as factoring or numerical methods.

4. How do numerical methods help in finding the roots of an equation?

Numerical methods use a series of calculations to approximate the roots of an equation. These methods are especially useful when the equation cannot be solved algebraically or when the roots are complex numbers.

5. Are there any limitations to finding the roots of an equation using methods?

Yes, some equations may have no real solutions, making it impossible to find the roots. Additionally, numerical methods may only provide an approximation of the roots and may not be completely accurate.

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