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Explore the Back-StoryTry this beautiful problem from Algebra based Roots of the cubic equation.

The polynomial has three positive integer roots. What is the smallest possible value of ?

Algebra

Vieta's Relation

roots of the equation

Answer:

AMC-10A (2010) Problem 19

Pre College Mathematics

The given equation is .we have to find out the smallest possible value of .From Vieta's Relation we know that if are the roots of equation then and

can you finish the problem........

Therefore is the sum of the three roots of the polynomial . and is the product of the three integer roots.Now the factors of =.there are only three roots to the polynomial so out of four roots we have to choose three roots such that two of the four prime factors must be multiplied so that we are left with three roots. To minimize , and should be multiplied,

can you finish the problem........

Therefore the value of =

- https://www.cheenta.com/ratio-of-two-triangles-amc-10a-2004-problem-20/
- https://www.youtube.com/watch?v=pYSIvF7jZy4

Try this beautiful problem from Algebra based Roots of the cubic equation.

The polynomial has three positive integer roots. What is the smallest possible value of ?

Algebra

Vieta's Relation

roots of the equation

Answer:

AMC-10A (2010) Problem 19

Pre College Mathematics

The given equation is .we have to find out the smallest possible value of .From Vieta's Relation we know that if are the roots of equation then and

can you finish the problem........

Therefore is the sum of the three roots of the polynomial . and is the product of the three integer roots.Now the factors of =.there are only three roots to the polynomial so out of four roots we have to choose three roots such that two of the four prime factors must be multiplied so that we are left with three roots. To minimize , and should be multiplied,

can you finish the problem........

Therefore the value of =

- https://www.cheenta.com/ratio-of-two-triangles-amc-10a-2004-problem-20/
- https://www.youtube.com/watch?v=pYSIvF7jZy4

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