subject: Square System Of Equations [print this page] Square system of equations is a Algebraic topic. And the square system of equations deals with algebraic expressions (that is it contains square terms)
Definition of a Square system of equations:-In linear system of equations the number of variables equal to the number of equations. The co-efficient of a matrix of a square matrix is a square matrix.
Example:-4x+9y=4
10x+12y=14
A polynomial is in the form ax2+bx+c, where a,b,c are real and complex numbers and a is not equal to 0. is called quadratic expression in the variable x.
ax2+bx+c In this quadratic expression "a" is the co-efficient of x2, and "b" is the co-efficient of x and "c" is the constant term. Here "ax2 " is the quadratic term and the "bx" is the linear term.
ax2+bx+c is the standard form of the quadratic equation. In this equation contains only one variable that is x.
The number b2-4ac is called the discriminant of the quadratic expression is ax2+bx+c. The discriminant is denoted by the ?.
?=b2-4ac
If a, are the roots of the quadratic equation ax2+bx+c =0 then a+ = (-b)/a and a = c/a
The quadratic equation having roots a, is (x-a) (x-) = 0 that is x2-(sum of the roots)x+ (product of the roots) =0
Extreme values of a square system equation:- Let f(x) =ax2+bx+c and x belongs to R,
(1)If a>0 then f(x) has minimum value (4ac-b2)/4a at x= (-b)/2a
(2)If a0, then the roots are real and unequal.
(2)?=b2-4ac=0, then the roots are real and equal.
(3)?=b2-4ac0 and ? is a perfect square then the roots are rational and unequal.
(2)?=b2-4ac>0 and ? is not a perfect square then the roots are irrational and unequal
(3)?=b2-4ac=0 then the roots are rational and equal
