The approximate solution to x³+5x²+6=0 is -5.23 after using the iteration formula.
What is iteration method?
Iteration is the process of repeating a procedure in order to produce a series of results.
We have an expression in three degree:
[tex]\rm x^3+5x^2+6=0[/tex]
The iteration formula:
[tex]\rm x_{n+1}=-5-\dfrac{6}{x^2_n}[/tex]
Starting with [tex]\rm x_1 = -1.5[/tex]
If we plug this value in the function, it will not satisfy the equation, so this is not a solution to the expression.
Plugging n = 1, and [tex]\rm x_1 = -1.5[/tex]
Plug this values in the iteration formula we get:
[tex]\rm x_2 = -7.666[/tex]
Similarly, plug n = 2, [tex]\rm x_2 = -7.666[/tex]
[tex]\rm x_3 =- 5.1020[/tex]
Plug n = 3, [tex]\rm x_3 = -5.1020[/tex]
[tex]\rm x_4 = -5.23[/tex]
Thus, the approximate solution to x³+5x²+6=0 is -5.23 after using the iteration formula.
Learn more about the iteration here:
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