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  Explain BISECTION METHOD (BOLZANO METHOD).  Engineering maths The method is applicable for numerically solving the equation  f ( x ) = 0 for the  real  variable  x , where  f  is a  continuous function  defined on an interval [ a ,  b ] and where  f ( a ) and  f ( b ) have opposite signs. In this case  a  and  b  are said to bracket a root since, by the  intermediate value theorem , the continuous function  f  must have at least one root in the interval ( a ,  b ). At each step the method divides the interval in two by computing the midpoint  c  = ( a + b ) / 2 of the interval and the value of the function  f ( c ) at that point. Unless  c  is itself a root (which is very unlikely, but possible) there are now only two possibilities: either  f ( a ) and  f ( c ) have opposite signs and bracket a root, or  f ( c ) and  f ( b...