Know the Fundamental Theorem of Algebra and verify it for quadratic polynomials.
Write a quadratic equation from two given roots
Problem
Find a monic quadratic equation whose roots are \(2\) and \(5\).
Big Picture
What this problem is really about
Building a monic quadratic from roots starts with one factor x minus r for each root. We’ll form both factors, expand their product, combine the middle terms, attach the equation to zero, and substitute each original root to verify the result.
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