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Find the roots of x⁴ - 10x² + 9 with NumPy.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Find the roots of with NumPy. Use np.poly to build the polynomial back from the roots, as a check. What is the value of the polynomial at , and what is the factorised form?
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. There is no and no term, so the coefficients are [1, 0, -10, 0, 9]. Sort and round the roots, as the roots come in any order.
Check. The roots are , and np.poly gives back [1, 0, -10, 0, 9] (the + 0.0 removes a possible ). At : . The factorised form is . By hand: .
Answer: roots . The value at 2 is . The factorised form is .
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