Algebra

Polynomial Factoring

Descartes Rule of Signs

         

Determine the number of sign changes in

M(x)=x6+x5+x2.M(x) = x^6 + x^5 + x - 2.

T(x)=x4+x3x21 T(x) = x^4 + x^3 - x^2 - 1

By determining the types sign changes in T(x)T(x) and T(x)T(-x), determine the number of non-real complex roots of T(x)T(x) .

Given that the equation x9x7+4x4+x2+100=0 x^9 - x^7 + 4 x^4 + x^2+100 = 0 has either 1, 5, or 9 real roots, determine the number of its positive roots.

Let J(x)=x54x4+x3+2x2+3J(x) = x^5 - 4x^4 + x^3 + 2x^2 + 3 . By comparing the values of J(1)J(1) and J(2)J(2) , find the number of real roots of J(x)=0 J(x) = 0 .

Is there any negative root to the polynomial

U(x)=x7+x7?U(x) = x^7 + x- 7 ?

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