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Polynomial Evaluation and Root Finding

A polynomial is an expression like ax² + bx + c (quadratic) or ax³ + bx² + cx + d (cubic). Evaluating means substituting a value for x. Finding roots means solving for x where the polynomial equals zero.

Methods for Finding Roots

Quadratic roots use the quadratic formula: x = (−b ± √(b²−4ac)) / 2a. Cubic roots use Cardano's method or trigonometric solutions. The discriminant determines whether roots are real or complex. Higher-degree polynomials generally require numerical methods.