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

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

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

with ${}a,b,c\geq 0$ and ${}d,e>0$ (hence, the coefficients of the polynomial, the accuracy ${}e$ and ${}1$ 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.

Create a solution