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Pure 2 Coursework Using Decimal search In this investigation, I have chosen x^5-14x+2=0. Such an equation cannot be solved algebraically. The following graph represents y= f(x): - Graph 1 - The graph shows me that x^5-14x+2=0 has three roots, lying in the intervals (-2,-1) , (0, 1) , (1,2). X -3 -2 -1 0 1 2 3 Y -199 -2 15 2 -11 6 203 Within the change of sign methods, decimal search method shall be used to find out an approximate value for roots of x^5-14x+2=0. In this method I first take increments of x of size 0.1 within the interval (1,2). I do this until I find a change in sign. X 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Y -11 -11.78 -12.31 -12.48 -12.22 -11.40 -9.91 -7.6 -4.3 0.16 There is a sign change, and therefore a root, in the interval (1.8,1.9). I can now continue with increments of 0.01 within the interval (1.8,1.9). X 1.8 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9 Y -4.3 -3.91 -3.51 -3.09 -2.66 -2.23 -1.77 -1.31 -0.83 -0.34 0.16 This shows that the root lies in the interval (1.89,1.90). We can express this information as, the root can be taken as 1.895 with maximum error of + 0.005 This can be...

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