Answer to Question #140001 in Quantitative Methods for xerin

Question

find the roots using bisector method. Stop until at 15th iteration or when approximate percent relative error is below 0.05%.

2x^4+13x^3+29x^2+27x+9=0

Answer 1

Solution. Find the roots using bisector method.

Find two points such that a < b and f(a)* f(b) < 0.

Find the midpoint of a and b, point m

If f(m) = 0 (m is root of the equation); else follow the next step

1) Divide the interval [a, b]

2) If f(m)*f(b) <0, let a =m

3) Else if f(m) *f(a), let b = m

Repeat steps until f(m) = 0 or relative error is below 0.05%.

$$ɛ_r=|\frac{x_{m,i+1}-x_{m,i}}{x_{m,i+1}}|\times100$$

Let a=-4 and b=-2.

As result first root is x₁=-3.

Let a=-2 and b=-1.2.

As result third root is x₂=-1.5.

The third root x₃=-1 cannot be found using the indicated method, since given the multiplicity of the root, the function to the right and left of the root takes positive values.

Answer. x₁=-3; x₂=-1.5; The third root x₃=-1 cannot be found using the indicated method, since given the multiplicity of the root, the function to the right and left of the root takes positive values.