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  • STRICTLY REAL FUNDAMENTAL THEOREM OF ALGEBRA USING POLYNOMIAL INTERLACING

  • Part of
  • SOHAM BASU
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 104 / Issue 2 / October 2021
    Published online by Cambridge University Press:
    18 January 2021, pp. 249-255
    Print publication:
    October 2021
    • Article
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  • Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses interlacing of bivariate polynomials similar to Gauss’s first proof of the fundamental theorem of algebra using complex numbers, but in a different context of division residues of strictly real polynomials. This shows the sufficiency of basic real analysis as the minimal platform to prove the fundamental theorem of algebra.