IOQM · Mathematics · Algebra
Roots and coefficients (Vieta), remainder/factor theorems, integer-root theorem, FTA at school level.
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Q1 · Polynomials · MEDIUM
Let p(x) be a monic polynomial of degree 3 such that p(1) = 1, p(2) = 4, and p(3) = 9. Find p(4).
Q2 · Polynomials · MEDIUM
Let p(x) = x³ - 7x + 6. If α, β, γ are the roots of p(x), find the value of α²β² + β²γ² + γ²α².