Math symbols
About us
Contact us
Site map
Search The Site
   Program of Lessons
 Study Guide
 Topics of problems
 Tests & exams
www.bymath.com Study Guide - Arithmetic Study Guide - Algebra Study Guide - Geometry Study Guide - Trigonometry Study Guide - Functions & Graphs Study Guide - Principles of Analysis Study Guide - Sets Study Guide - Probability Study Guide - Analytic Geometry Select topic of problems Select test & exam Rules Price-list Registration

Properties of roots of a quadratic equation. Viete’s theorem

Roots of quadratic equation. Discriminant. Viete's theorem.

The formula



shows, that the three cases are possible:


           1)  b 2   4 a c > 0 ,  then two roots are different real numbers;


           2)  b 2   4 a c = 0 ,  then two roots are equal real numbers;


           3)  b 2   4 a c < 0 ,  then two roots are imaginary numbers.


The expression  b 2  4 a c , value of which permits to differ these three cases, is called a discriminant of a quadratic equation and marked as D.


Viete’s theorem. A sum of roots of reduced quadratic equation x2 + px + q = 0 is equal to coefficient at the first power of unknown, taken with a back sign, i.e.                                                    


 x1x2 = p ,


and a product of the roots is equal to a free term, i.e.


x1  ·  x2  =  q .


To prove Viete’s theorem, use the formula, by which roots of reduced quadratic equation are calculated.


| Home | About us | Links | Contact us |

Copyright © 2002-2007 Dr. Yury Berengard.  All rights reserved.