Solution for Polynomial Degree 7: x2=k2-k2x7/2

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The discussion centers on solving the polynomial equation x2 = k2 - k2x7/2. By substituting y = x1/2, the equation transforms into y4 = k2 - k2y7, leading to the polynomial k2y7 + y4 - k2 = 0. The discussion highlights that factoring this polynomial is complex, and it is established that solutions for polynomial equations of degree higher than 4 cannot be expressed using algebraic functions. Additionally, the conversation touches on the existence of formulas for the sum of products of roots.

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chhitiz
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can anyone tell me the solution of- x2=k2-k2x7/2
 
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(Is that first "-" a minus or a hyphen?)

If you let y= x1/2, x2= k2- k2x7/2 becomes y4= k2- k2y7 or k2y7+ y4- k2= 0. I see no simple way to factor that and, in general, solutions to polynomial equations of degree higher than 4 cannot be written in terms of algebraic functions.
 
i got that far as well. isn't there a formula for sum of product of roots n at a time, n-1 at a time and so on?
 

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