### Mathematics Class X

Real Numbers
Polynomials
Arithmetic Progressions
Triangles
Coordinate Geometry
Introduction to Trigonometry
Circles
Constructions
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability

# Methods to solve the Quadratic Equations

There are three methods to solve the Quadratic Equations-

1. Factorization Method

In this method, we factorize the equation into two linear factors and equate each factor to zero to find the roots of the given equation.

Step 1: Given Quadratic Equation in the form of [mathtype]  .

Step 2: Split the middle term bx as mx + nx so that the sum of m and n is equal to b and the product of m and n is equal to ac.

Step 3: By factorization we get the two linear factors (x + p) and (x + q)

[mathtype]  = (x + p) (x + q) = 0

Step 4: Now we have to equate each factor to zero to find the value of x.

[mathtype]

These values of x are the two roots of the given Quadratic Equation.

1. Completing the square method

In this method, we convert the equation in the square form [mathtype]  to find the roots.

Step1: Given Quadratic Equation in the standard form [mathtype]  .

Step 2: Divide both sides by a

[mathtype]

Step 3: Transfer the constant on RHS then add square of the half of the coefficient of x i.e. [mathtype]  on both sides

[mathtype]

[mathtype]

Step 4: Now write LHS as perfect square and simplify the RHS.

[mathtype]

Step 5: Take the square root on both the sides.

[mathtype]

Step 6: Now shift all the constant terms to the RHS and we can calculate the value of x as there is no variable at the RHS.

[mathtype]