Question

Find the root of the following function using bisection method: x 2-3=0

Answer 1

x^2 -3

when x=1 then f(1) = -2

and when x=2 then f(2)=1

so the root must lie within x=1 and x=2,

so taking x=(1+2)/2 = 1.5, we get f(1.5)= -0.75

so root lies between x=1.5 and x=2, so taking x = (1.5+2)/2 = 1.75, we get f(1.75) = 0.0625

now taking x = (1.5 + 1.75)/2 = 1.625 and plugging into f and repeating the steps we can get as close to root(3) as much we require.

Similarly, we can proceed with x=-1 and x=-2 to get close to -root(3)