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Key Concepts
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1. Degree of a Polynomial
The highest power of x in a polynomial p(x) is called the degree of the polynomial.
- Linear: Degree 1
- Quadratic: Degree 2
- Cubic: Degree 3
2. Zeros of a Polynomial
A real number k is said to be a zero of a polynomial p(x) if p(k) = 0. Geometrically, the zeros are the x-coordinates of the points where the graph intersects the x-axis.
3. Relationship between Zeros and Coefficients
For a quadratic polynomial ax² + bx + c:
For a cubic polynomial ax³ + bx² + cx + d:
- α + β + γ = -b/a
- αβ + βγ + γα = c/a
- αβγ = -d/a