QUADRATIC EQUATIONS www.mathguide.org

QUADRATIC EQUATION A polynomial of degree two is called quadratic polynomial General form of quadratic polynomial is ax2+bx+c, a,b,c are real numbers and a≠0. If for x= α, α ϵ R, the value of quadratic polynomial becomes zero, then α is called zero of the quadratic polynomial. The equation ax2+bx+c=0, a≠0 is called quadratic equation. If α and β are two zeros of ax2+bx+c=0, then we say that α and β are roots of the quadratic equation.

For quadratic equation ax2+bx+c=0, a≠0, roots are given by GENERAL FORMULA TO FIND OUT ROOTS OF A QUADRATIC EQUATION or QUADRATIC FORMULA For quadratic equation ax2+bx+c=0, a≠0, roots are given by x= −b± b 2 −4ac 2a

LINEAR EQUATION IN TWO VARIABLES A linear equation with two variables is called linear equation in two variable say x and y but the highest degree of each variable is one. Linear equation of the form ax+by+c=0 is called linear equation in two variables. Pair of values, one for x and one for y which satisfies the equation is called the solution or roots of linear equation in two variables. Linear equation in two variables represent a straight line on the graph with x and y as coordinates of the point (say P) on the line. x is called abscissa and y is called ordinate of P

Points to remember: b 2 −4ac is called Discriminant denoted by D i.e. D= b 2 −4ac. This discriminant helps to understand the nature of roots of quadratic equation. If D = 0, the roots of quadratic equation are Real and Equal. x = - b 2a , - b 2a i.e. α = - b 2a and β = - b 2a If D>0, the roots of quadratic equation are Real and Distinct. i.e . α= −b+ b 2 −4ac 2a , β= −b− b 2 −4ac 2a If D<0, the roots of quadratic equation are Imaginary.