Answer to Question #140000 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%.

3x^4-8x^3-37x^2+2x+40

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%.

$$ɛ_r=|{\frac{x_{m,i+1}-x_{m,i}}{x_{m,i+1}}}|\times 100$$

Let a=4 and b=6

As result first root is x₁=5.

Let a=0 and b=2

As result second root is x₂=1.

Let a=-2.5 and b=-1.5

As result third root is x₃=-2.

Let a=-1.5 and b=-0.5

For the eleventh iteration approximate percent relative error is below 0.05%. Therefore the fourth root is

$$x_4=-1.3335$$

Answer. x₁=5; x₂=1; x₃=-2; x₄=-1.3335.