SOLUTION: Show that the product of the roots of a quadratic equation is c/a.

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Question 1208778: Show that the product of the roots of a quadratic equation is c/a.
Found 3 solutions by Shin123, math_tutor2020, ikleyn:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
By the quadratic formula, the roots of the quadratic ax%5E2%2Bbx%2Bc are x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a. Multiplying these together gives . To simplify the numerator, we recall the difference of squares factorization, which is %28x-y%29%28x%2By%29=x%5E2-y%5E2 (this can be proved by expanding the left side). Therefore, the product of the roots is , so we are done.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

This has been answered previously at this link here
https://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.1207450.html
Let me know if you have any questions.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is well known theorem (formula) by French mathematician Vieta,
discovered by him in the 16th century (somewhen in the years 15xy).

Any relevant Algebra textbook contains it and explains it.

See this Wikipedia article
https://en.wikipedia.org/wiki/Vieta%27s_formulas