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I love you guys this is work that I run out taking you through this tutorial on relocation in numerical methods using sine change so when there is no direct method of solving any push an attempt may be made to first locate the roots so now suppose we wish to solve the equation FX equal to 0 where FX means function of its it was 0 the root will lie between two values of x for which FX changes signs in other words if they if they realize between X got a and X equal to B it means are the product of FB fa times FB will be quote will be less than 0 why is it less than 0 it means because and positive value x negative value will give a negative value and we all know that negative values are always less than 0 so in this case if f is positive FB will be negative is there to be a sign change and the reverse is true so if this condition holds it means that there is a root between those two values a and B so that is the condition we shall use to locate roots so problem one says locate each of the