How Do You Calculate the Square Root of a Polynomial?

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SUMMARY

The discussion focuses on the impossibility of calculating the square root of the polynomial 4x4 + 8x3 + 8x2 + 4x + 1. It is established that for a polynomial q(x) to have a square root p(x), the roots of q must have even multiplicities, which is not the case for the given polynomial. The suggested approach involves assuming p(x) as ax2 + bx + c, squaring it, and equating coefficients with q, leading to a system of equations that has no solution.

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does anyone know any specific method to find the square root of a polynomial like : 4x4 + 8x3 + 8x2 + 4x+ 1 ??
thanks in advance!
 
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You want to find a polynomial p(x) such that [p(x)]2 = q(x)?
If this is it, it is not possible, for a general q, to find p. q must have roots with even multiplicities. This is not the case in your example. Try putting p = ax2+bx+c, square it, and equate coefficients with q. You'll find a system of equations with no solution.
 

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