+249 Marcelle and Jaclyn each think of a polynomial. Each of their polynomials is monic, has degree 4, and has the same positive constant term and the same coefficient of z. The product of their polynomials is z^8 +3z^7 +z^6 +3z^5 +4z^4 +6z^3 +2z^2 +4. What is the constant term of Jaclyn's polynomial?
+118677 Hi Higgsb :)
Marcelle and Jaclyn each think of a polynomial. Each of their polynomials is monic, has degree 4, and has the same positive constant term and the same coefficient of z.
Marcelle \(z^4+az^3+bz^2+cz+k\)
Jaclyn \(z^4+pz^3+qz^2+cz+k\)
The product of their polynomials is \(z^8 +3z^7 +z^6 +3z^5 +4z^4 +6z^3 +2z^2 +4\)
What is the constant term of Jaclyn's polynomial?
k^2 = 4 so k= +2 or k=-2 but k is positive so
The constant is 2
The coefficient of z is not relevant.
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