Math Problem Statement
write a polynomial equation with integer coefficients that has the given roots y=3, y=-1, y=3
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Roots of Equations
Formulas
For each root r, the factor is (y - r)
(y - 3)^2 (since y=3 is a repeated root)
(y + 1) for y = -1
Expanding: (y^2 - 6y + 9)(y + 1) = y^3 - 5y^2 + 3y + 9
Theorems
Fundamental Theorem of Algebra
Suitable Grade Level
Grades 9-12