MATH152 April 2017
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Question A 22
Describe all cubic polynomials passing through the points
, , and .
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Substitute into the equation to get an equation of unknowns . Repeat the same for .
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Substitute into the equation, we have .
Substitute into the equation, we have
When , we have .
Solving these equations, we have .
Thus, any cubic polynomials with coefficients satisfying are the desired polynomials.
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