Revision: Algebra Mathematics SSLC (English Medium) Class 10 Tamil Nadu Board of Secondary Education

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

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”

• A quadratic equation has degree 2.
• Its standard form is \[ ax^2 + bx + c = 0, \] where \[ a \neq 0. \]
• A root is a value of \[ x \] that satisfies the equation.
• A quadratic equation has at most two roots.

• Matrix: A rectangular array of elements.

• Element: An entry inside a matrix.

• Order: Size of a matrix written as rows × columns.

• Row: Horizontal set of elements.

• Column: Vertical set of elements.

• a_ij​: Element in the i-th row and j-th column.