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Pure 2 Coursework Decimal Search This method works by drawing a graph, seeing where it crosses the axis, then re-plotting the graph, with a smaller scale. This is repeated until required accuracy is achieved. I require an accuracy of four decimal places. The equation I shall investigate will be: y = x4+2x3-5x2+1 I shall find the root by working out values of x and looking for a change of sign. I can see by looking at the graph that the change of sign occurs between 3 and 4. I shall plot a graph, to find a more accurate estimate. x f(x) -4 49 -3 -17 -2 -19 -1 -5 0 1 1 -1 2 13 3 91 I can now see that the change of sign occurs between 3.4 and 3.5. Again, I shall draw another graph to find a more accurate answer. x f(x) -3 -17 -3.1 -14.2799 -3.2 -10.8784 -3.3 -6.7319 -3.4 -1.7744 -3.5 4.0625 -3.6 10.8496 -3.7 18.6601 x f(x) -3.4 -1.7744 -3.41 -1.23143 -3.42 -0.6796 -3.43 -0.11884 -3.44 0.450921 -3.45 1.029756 -3.46 1.617735 -3.47 2.214927 x f(x) -3.43 -0.11884 -3.431 -0.06227 -3.432 -0.00561 -3.433 0.051138 -3.434 0.107979 -3.435 0.16491 -3.436 0.221931 -3.437 0.279043 Solution = -3.4325 ± 0.0005 f (-3.432) = -0.00561 f (-3.433) = 0.051138 Change of sign indicates a root...

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