You are here:

- Home
- Science
- Mathematics
- Advanced Math
- Quadratic equations

Advertisement

This problem might be one of the hardest polynomial problems, I have encountered. Any help you can offer would be appreciated.

Given 26 equations in the form (x^2)+ax+c. The coefficients of x in the 26 respective equations have values: -1, -3, -5, -7 ...-51

If the roots of each equation are consecutive integers, find the sum of the squares of the 52 roots of the 26 equations. (2 roots per equation)

Questioner: Isaac

Country: Illinois, United States

Category: Advanced Math

Private: No <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< changed

Subject: difficult polynomial problem

Question: This problem might be one of the hardest polynomial problems, I have encountered. Any help you can offer would be appreciated.

Given 26 equations in the form (x^2)+ax+c. The coefficients

of x in the 26 respective equations have values: -1, -3, -5,

-7 ...-51

If the roots of each equation are consecutive integers, find

the sum of the squares of the 52 roots of the 26 equations.

(2 roots per equation)

............................

Have you studied quadratic equations? Then you learned that

in the equation:

x^2 + ax + c

the sum of the roots is equal to -a.

Thus if the equation is:

x^2 - 5x + c = 0. <<<<< don't leave out the "= 0"

then the roots add up to 5. If that is so, then you have a

basic algebra problem:

Find two consecutive integers whose sum is 5.

Your little sister could do that one.

So you have:

Find two consecutive integers whose sum is 1.

Find two consecutive integers whose sum is 3.

Find two consecutive integers whose sum is 5.

......

Find two consecutive integers whose sum is 51.

I think you can take it from there.

P.S. You will need the (well-known) formula for the sum of

the squares of the first 'n' integers.

Advanced Math

Answers by Expert:

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.**Education/Credentials**

-----------