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Solving Polynomial Equations

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This article delves into the concept of real roots in polynomial equations, illustrating how these roots correspond to the x-coordinates of the points of intersection (PoIs) of two functions. It emphasizes the fact that a polynomial equation of degree "n" has "n" complex roots but at most "n" real roots. The exploration includes examples showing how complex roots can be real, imaginary, or a mixture and highlights the relationship between real roots and zeros of combined functions.

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Solving Polynomial Equations

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  1. Solving Polynomial Equations Determining the Real Roots of an Equation is equivalent to Determining the x-coords of the PoIs of 2 Functions which is also equivalent to Determining the Zeros of a Combined Function

  2. REAL ROOTS OF EQN = X-COORDS OF POIS = ZEROS OF FN

  3. REAL ROOTS OF EQN = X-COORDS OF PoIs = ZEROS OF FN

  4. REAL ROOTS OF EQN = X-COORDS OF POIS = ZEROS OF FN A polynomial equation of degree “n” has “n” complex roots but will have AT MOST “n” real roots! Complex roots may be all real (“a”) or all imaginary (“± bi”) or a mixture (“a ± bi”).

  5. REAL ROOTS OF EQN = X-COORDS OF PoIs = ZEROS OF FN Ex#3] Ex#4] or or  the real roots are  the real roots are

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