Real polynomial/Degree 3/Positive coefficients/Zero/Pseudocode/Program/Exercise

Write a computer-program (in pseudocode) which for a polynomial ${\displaystyle {}dX^{3}+cX^{2}+bX+a}$ of degree ${\displaystyle {}3}$ computes a zero within an accuracy of a given number ${\displaystyle {}e>0}$ berechnet.

• The computer has as many memory units as needed, which can contain nonnegative real numbers.
• It can write the content of a memory unit into another memory unit.
• It can halve the content of a memory unit and write the result into another memory unit.
• It can add the content of two memory units and write the result into another memory unit.
• It can multiply the content of two memory units and write the result into another memory unit.
• It can compare the content of memory units and can, depending on the outcome, switch to a certain program line.
• It can print contents of memory units and it can print given texts.
• There is a stop command.

The initial configuration is

${\displaystyle (a,b,c,d,e,1,0,0,\ldots )}$

with ${\displaystyle {}a,b,c\geq 0}$ and ${\displaystyle {}d,e>0}$ (hence, the coefficients of the polynomial, the accuracy ${\displaystyle {}e}$ and ${\displaystyle {}1}$ are in the first memory units).

The program shall print a sentence telling the bounds of an interval for a zero with the wished-for accuracy and stop.