Question

Are every quintic equation convertible into Bring Jerrard's quintic form? If yes, then how? Please give a detailed solution

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Answer 1

Answer:

Step-by-step explanation:

The value of –1 <= cosθ <=1

So, there is no real θ for which the value of cosθ = 4.996.

So, the complex and imaginary solution for the above question is θ = ±2.2916i

where, i = √(–1)

Refer the attachment for the solution

And, the value of θ for cosθ = 0.4996

=> θ = 60° 1' 35''

Answer 2

Step-by-step explanation:

The objective of this paper is to add further to the research into the solution quintic of equations that has preoccupied

mathematicians for centuries.

Quintic equations are part of polynomial equations. From literature [1, 2] polynomial equations were first investigated more

than four thousand years ago.

The general quintic equation takes the form 5432

4 3 2 10 x ax ax ax ax a + + + + += 0 1

Abel and Ruffini showed that proved that it impossible to solve over a field of rational numbers, Rosen [3]

Bring [4] and Jerrard [5] have shown that the equation can be reduced to a simple form with two parameters. That is,

5 x px q + += 0 2

The equation 2 above is now called the Bring-Jerrard quintic equation, a trinomial form of the general quintic equation.

Glashan [6], Young [7], Runge [8] showed that some form of the Bring-Jerrard quintic equation is solvable in radicals. Spearman

and William [9] came with similar results.

Many others contributed in various ways.

Motlotle [10], in his 2011 master’s thesis managed to present a formula for solving the Bring-Jerrard quintic equation using

the Newton’s sum formula. In his contribution Motlotle convincingly argued that Abel’s impossibility proof has been misconstrued

by many as meaning that no general algebraic solution of the quintic equation is attainable. He showed that such a formula in

unattainable only within a field of Rational numbers. He then moved on to deriving a formu