There are three methods to solve the Quadratic Equations-
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.
These values of x are the two roots of the given Quadratic Equation.
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
Step 3: Transfer the constant on RHS then add square of the half of the coefficient of x i.e. [mathtype] on both sides
Step 4: Now write LHS as perfect square and simplify the RHS.
Step 5: Take the square root on both the sides.
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.
In this method, we can find the roots by using quadratic formula. The quadratic formula is
where a, b and c are the real numbers and b2 – 4ac is called discriminant.
To find the roots of the equation, put the value of a, b and c in the quadratic formula.