Quadratic Equations

An equation with one variable, in which the highest power of the variable is two, is known as a quadratic equation.

Standard Form:

 ax² + bx + c = 0,  a ≠ 0

For example :

(i) 3x² + 4x + 7 = 0

(ii) 4x² + 5x = 0 

A value of the variable which satisfies the equation is called a root (solution).

If substituting a value of x makes the polynomial zero, that value is a root.

• A number α is called a root of ax² + bx + c = 0, if aα² + bα + c = 0

The set of elements representing the roots of a quadratic equation is called its solution set.

If a quadratic equation contains only two terms where one is a square term and the other is the first power term of the unknown, it is called adjected quadratic equation.

For example :

(i) 4x² + 5x = 0

(ii) 7x² − 3x = 0, etc. 

If the quadratic equation contains only the square of the unknown, it is called a pure quadratic equation.

For example :

(i) x² = 4 

(ii) 3x² − 8 = 0, etc.