How to solve 4x3 plus 0.4x2 plus 0.01x-2.4x10-18 equals 0?

Answer 1

There are a number of ways. One possibility is the iterative method.

Rewrite the equation so as to make x the subject:

4x3 + 0.4x2 + 0.01x - 2.4*10-18 = 0

4x3 = 2.4*10-18 - 0.4x2 - 0.01x

x3 = (2.4*10-18 - 0.4x2 - 0.01x)/4 x = cuberoot[(2.4*10-18 - 0.4x2 - 0.01x)/4]

The original equation is approximately equal to

4x3 + 0.4x2 + 0.01x = 0

or x*(20x - 1)2 = 0

which has roots at x = 0 and x = -0.05

Start with a value, x1 near one of these roots and use the iteration:

xn+1 = cuberoot[(2.4*10-18 - 0.4xn2 - 0.01xn)/4] where n = 1, 2, 3, etc to improve your estimates.

The resulting roots are, not surprisingly, 0 and -0.05 to 10 decimal places.