Question

3x=sqrt(1+sinx) by bisection method

Answer 1

Answer:

This is a cubic, not a quadratic equation.

The bisection method finds two values of x that make f(x)<0 and f(x)>0, then we change x so that it's the average of both attempts. The iterative method allows us to find such values for x.

When f(2)=-1 and f(3)=16 so there is a root between x=2 and 3, so now put x=2.5:

f(2.5)=5.625 so now we average 2 and 2.5=2.25. f(2.25)=1.89 approx, so we average 2 and 2.25=2.125.

f(2.125)>0 so we continue in the same way, finally arriving at x=2.0945 approx.

Another initial approach is to draw the graph of f(x) and note that it intersects the x-axis close to 2.1. This enables you to see what initial values of x to use.