Writing Polynomials from Roots

Algebra 2 · Axiom Academy

EXAMPLE Writing a Polynomial with Roots Construct a real-coefficient polynomial when given its roots, including a complex-conjugate pair. Write a polynomial with real coefficients that has roots 2 , -1+i , and -1-i . Excellent work! You've successfully constructed a polynomial from its roots. Remember: Complex conjugates always appear in pairs when the polynomial has real coefficients. Use the factor form: if r is a root, then (x - r) is a factor. Multiply conjugates first: this produces a real quadratic factor. The pattern (a+bi)(a-bi) = a^2+b^2 is essential for working with conjugates. Final degree equals the number of roots: three roots give a cubic polynomial. This method works for any set of roots, real or complex. Always look for conjugate pairs first to simplify your work!

This is the written version of the interactive lesson above. See the full Algebra 2 course.