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Imaginary zeros of polynomials
- Lesson: 18:12
- Lesson: 27:19
Imaginary zeros of polynomials
Lessons
Based on the quadratic formula 2a−b±b2−4ac , non-real roots occur when the discriminant,
b2−4ac , is negative. Non-real roots always occur in pairs.
- 1.Discussing the Relationship Between the Discriminant and X-intercepts on a Graph
Sketch and compare the following quadratic functions:
i) y=2x2+x−15
ii) y=x2+4x+4
iii) y=2x2+x+15 - 2.Locating the Regions of Imaginary Zeros on Polynomial Graphs
Indicate the region on the graphs where the non-real zeros occur.
i) f(x)=101(x+2)(x−1)(x−3)(x−5)
ii) g(x)=101(x+2)(x−1)(x2−8x+17)
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3.
Polynomial Functions
3.1
What is a polynomial function?
3.2
Polynomial long division
3.3
Polynomial synthetic division
3.4
Remainder theorem
3.5
Factor theorem
3.6
Rational zero theorem
3.7
Characteristics of polynomial graphs
3.8
Multiplicities of polynomials
3.9
Imaginary zeros of polynomials
3.10
Determining the equation of a polynomial function
3.11
Applications of polynomial functions
3.12
Solving polynomial inequalities
3.13
Fundamental theorem of algebra
3.14
Descartes' rule of signs