7D - Methods for solving polynomial equations
Using CAS to solve polynomial equations:
Polynomial equations can be solved using the solve command on the CAS calculator. To use the command:
Polynomial equations can be solved using the solve command on the CAS calculator. To use the command:
Highlight the equation → Interactive → Equation/inequality → Solve
Make sure the variable you are solving for is listed on the screen (to change the variable use the Var keyboard).
7D - Example 1: Using CAS to solve polynomial equations (CAS)
Solve the equation \(3w^4-w^3-10w^2=-2w-8\) for \(w\) using a CAS calculator.
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7D - Example 1: Video solution
7D - Example 1: Practice
Question 1: ABC Question 2: ABC 7D - Example 1: Solutions
Question 1: ABC Question 2: ABC |
Using the null factor law to solve polynomial equations:
Similar to quadratics, we can use the null factor law to solve cubic and quartic equations.
Similar to quadratics, we can use the null factor law to solve cubic and quartic equations.
■ The null factor law state that if \(a\times b=0\), then \(a=0\), \(b=0\) or \(a=b=0\).
The null factor law can be used to solve cubic and quartic equations. To solve a polynomial equation:
- Manipulate the equation so that the polynomial equation is equal to zero; that is, \(ax^n+...+b=0\).
- Use the rational root theorem to identify linear factors of the polynomial.
- Use long division or synthetic division to help factorise the polynomial
- Use the null factor law to find the solution(s).
7D - Example 2: Solving polynomial equations
Solve the equation \((3x-1)(x-3)(x+1)(x+2)=0\) for \(x\).
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7D - Example 2: Video solution
7D - Example 2: Practice
Question 1: ABC Question 2: ABC 7D - Example 2: Solutions
Question 1: ABC Question 2: ABC |
7D - Example 3: Solving polynomial equations
Consider the polynomial \(P(x)=2x^3+7x^2+x-10\).
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7D - Example 3: Video solution
7D - Example 3: Practice
Question 1: ABC Question 2: ABC 7D - Example 3: Solutions
Question 1: ABC Question 2: ABC |