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Rational zero theorem
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Rational zero theorem
What is rational zeros theorem? It is sometimes also called rational zero test or rational root test. We can use it to find zeros of the polynomial function. It is used to find out if a polynomial has rational zeros/roots. It also gives a complete list of possible rational roots of the polynomial. It also comes in handy when we need to factor a polynomial alongside with the use of polynomial long division or synthetic division.
Basic Concepts: Solving quadratic equations by completing the square, Solving quadratic equations using the quadratic formula, Nature of roots of quadratic equations: The discriminant
Related Concepts: Integration of rational functions by partial fractions
Lessons
Rational Zero Theorem:

- IntroductionIntroduction to Rational Zero Theorem
- 1.Consider the polynomial P(x)=9x3+6x2−29x−10a)Determine the potential zerosb)Factor P(x) fully.c)Solve the equation: 9x3+6x2−29x−10=0
- 2.Solve the equation: x4−5x3+22x−12=0
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4.
Polynomial Functions
4.1
What is a polynomial function?
4.2
Polynomial long division
4.3
Polynomial synthetic division
4.4
Remainder theorem
4.5
Factor theorem
4.6
Rational zero theorem
4.7
Characteristics of polynomial graphs
4.8
Multiplicities of polynomials
4.9
Imaginary zeros of polynomials
4.10
Determining the equation of a polynomial function
4.11
Applications of polynomial functions
4.12
Solving polynomial inequalities
4.13
Fundamental theorem of algebra
4.14
Descartes' rule of signs