How to find first root of cubic equation or first zero of cubic polynomial?

Please find attached the proof and method with example.
Your views about usefulness or preference to other methods is most welcome.

How to write prime numbers up to a certain number?

(1) Suppose you want to write prime numbers  upto a= 100.
Take square root of a=100. It is 10. Take integer part of it if a is not a perfect square.
In other words find the largest perfect square b less than or equal to this number a.  Find square root of this perfect square, say c.
(2) Select the greatest prime number e less than or equal to this square root i.e. c here 10, so e is 7 since 10, 9 & 8 are composite. 
(3) Now start writing. In first step write 2 and 3.
(4) This method is based on the fact that every prime number which is greater than 3 can be expressed as 6K + 1.
(5) Divide a= 100 by 6.
(6) Take integer part of quotient,  i.e. answer of division say d.
(7) Write those many (d) multiples of 6 living some space on the left side and right of it one  below the other.
(8) Write natural numbers before and after the multiples of 6.
(9) According to me, multiples of 2 and 3 are the most occurring numbers so 2x3=6.
(10) Cancel all multiples of prime number to next 3 i.e. multiples of 5.
(11) After this step you are able to see some prime numbers.
(12) Cancel all the multiples of prime number next to 5 i.e. 7. Here you can use trick. Find answers of multiplication (products) of 7 with prime numbers next to 7. i.e. 7 x 11=77, 7 x 13 = 91. For this step you can use prime numbers obtained so far in previous step.
(13) Continue the process of cancellation till you reach e. In other words if c is a composite number then continue previous step till you get greatest prime number less than c. If c is a prime then continue till c.
(14) You are ready with the required prime numbers. 