Definitions [6]
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
The set of elements representing the roots of a quadratic equation is called its solution set.
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
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.
A matrix is a rectangular arrangement of numbers arranged in rows and columns, enclosed in brackets [ ] or parentheses ( ).
Elements (Entries) of a Matrix
- Each number in a matrix is called an element (or entry).
Rows and Columns
- Horizontal lines → rows
- Vertical lines → columns
Order of a Matrix
- Order = number of rows × number of columns
- Written as m × n and read as “m by n”
