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  • Mathematics
    Algebra: Polynomial Roots
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                      Polynomila Roots

                      For a given polynomial p(x) = an xn + an-1 xn-1 + ... + a1 x + a0 , of a single variable x and with the real coeffiecints an, an-1, ... , a1, a0 . ( ai ∈ ℝ , i=0, ... , n ) ,
                      find the the roots xn, xn-1, ... , x1 such that p(x) = (x - xn)(x - xn-1)...(x - x2)(x - x1)
                      In other words, find all xi such that p(xi) = 0 , where i=1, ... , n, and n is a degree of a polynomial p.
                      Please Note:
                      • For polynomials of degrees 1, 2 and 3, we will calculate the exact roots. For polynomials of degrees 4 and higher,
                        we might need to use numeriacl methods to find closest values to the actual roots.
                      • Use only explicit real numbers for coefficients, no parameters or variables are allowed.
                      • The default polynomial variable is x but you can choose any other.
                      • To raise the variable to the power of n (where n must be an explict positive integer), use the operator ^
                      • as in X^2
                      Please enter the polynomial whose roots you are looking for:p( ) =