Polynomials and Rational Expressions Question
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Grade 11 Polynomials and Rational Expressions CCSS: HSN-CN.C.9
Looking at the graph of a quadratic polynomial, roots or zeros correspond to where the graph crosses the x-axis. When the graph just touches the x-axis, this corresponds to a double root. The Fundamental Theorem of Algebra states that a quadratic polynomial will always have 2 roots. How is this reconciled with a quadratic polynomial whose graph does not intersect the x-axis?
- Quadratic polynomials always intersect the x-axis.
- If a quadratic polynomial doesn't cross the x-axis it is no longer a polynomial, and the Fundamental Theorem of Algebra no longer applies.
- When a quadratic polynomial doesn't cross the x-axis, this simply implies that its roots are complex with non-zero imaginary parts.
- Simply translate the quadratic polynomial till it does cross the x-axis.