There are three methods to solve the Quadratic Equations-

**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.

**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]

**Quadratic formula method**

In this method, we can find the roots by using quadratic formula. The quadratic formula is

[mathtype]

where a, b and c are the real numbers and b^{2 }– 4ac is called discriminant.

To find the roots of the equation, put the value of a, b and c in the quadratic formula.

Login

Accessing this course requires a login. Please enter your credentials below!