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Polynomials are essential mathematical expressions characterized by their degrees. This chapter explores the definitions, types, and geometric interpretations of polynomials, particularly focusing on their zeroes and the relationship between zeroes and coefficients. It also discusses the division algorithm for polynomials and highlights key concepts through various examples.
Chapter 25 sections
Polynomials are essential mathematical expressions characterized by their degrees. This chapter explores the definitions, types, and geometric interpretations of polynomials, particularly focusing on their zeroes and the relationship between zeroes and coefficients. It also discusses the division algorithm for polynomials and highlights key concepts through various examples.
Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.
A quadratic polynomial in x with real coefficients is of the form ax2 + bx + c, where a, b, and c are real numbers with a ≠ 0.
The zeroes of a polynomial p(x) correspond to the x-coordinates of points where the graph of y = p(x) intersects the x-axis.
A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.
If α and β are the zeroes of a quadratic polynomial ax2 + bx + c, then the relationships are given by -b/a = α + β and c/a = αβ.
For cubic polynomials, there are established relationships among the coefficients and zeroes: -b/a = α + β + γ, c/a = αβ + βγ + γα, and -d/a = αβγ.
An expression consisting of variables raised to whole number powers, combined using addition, subtraction, multiplication, and coefficients.
A polynomial of degree 1 that has the general form ax + b.
A polynomial of degree 2 expressed in the form ax2 + bx + c where a ≠ 0.
A polynomial of degree 3 expressed in the form ax3 + bx2 + cx + d where a ≠ 0.
The values of x that make the polynomial equal to zero, represented by the x-coordinates where the graph intersects the x-axis.
Total Questions
2
Estimated Time
4 min
Passing Score
70%
2 more questions available