Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991 Association of Mizar Users

Jan Popiolek
Warsaw University, Bialystok

### Summary.

Consider a quadratic trinomial of the form \$P(x)=ax^2+bx+c\$, where \$a\ne 0\$. The determinant of the equation \$P(x)=0\$ is of the form \$\Delta(a,b,c)=b^2-4ac\$. We prove several quadratic inequalities when \$\Delta(a,b,c)<0\$, \$\Delta(a,b,c)=0\$ and \$\Delta(a,b,c)>0\$.

#### MML Identifier: QUIN_1

The terminology and notation used in this paper have been introduced in the following articles [1] [2]

Contents (PDF format)

#### Bibliography

[1] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Andrzej Trybulec and Czeslaw Bylinski. Some properties of real numbers operations: min, max, square, and square root. Journal of Formalized Mathematics, 1, 1989.