You are given the function f(x)=x^3-x^2-7x+3, and that x=3 is a root of f(x)=0. Find the exact values of the other 2 roots. (6 marks)
First step is to realise that as x=3 is a root of f(x)=0, then we can use (x-3) as a factor of f(x). A really good method to use to find what (fx)/(x-3) gives is Synthetic Division. Using this method we then find that f(x)/(x-3) = x^2+2x-1. Next step is to use the quadractic we found to find the two roots of original f(x). Competing the square or using the quadratic formula are both good options to use, however completing the square gives a nice simplified answer a little faster, and removes the chance of not forgetting to simplify the final answer and losing marks in the exam. The other two roots are -1±sqrt(2).
DH
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