Let f(x)=xn+a1xn−1+⋯+an, where a1,a2,…,an are given numbers. It is given that f(x) can be written in the form f(x)=(x+k1)(x+k2)⋯(x+kn).
- By considering f(0), or otherwise, show that k1k2…kn=an.
- Show also that (k1+1)(k2+1)⋯(kn+1)=1+a1+a2+⋯+an and give a corresponding result for (k1−1)(k2−1)⋯(kn−1).
- Find the roots of the equation x4+22x3+172x2+552x+576=0, given that they are all integers.
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