Let us consider a quadratic equation where a is not equal to zero.
Let us use completing the square method in this general equation.
BydividingaonbothLHSandRHS,weget:
On taking LCM, we get and in denominator and numerator respectively.
Let us bring from left hand side to right hand side.
Here, we are going to assume that is greater than or equal to zero. Note that it can't be less than 1 because since it is negative, the roots becomes unreal. On taking square roots, we get:
From this we can say that the roots of the quadratic equation are:
and
This formula for finding the roots of the quadratic equation is called as quadratic formula.
Answers & Comments
Answer:
this is the derivation of quadratic formula
Solution:
Let us consider a quadratic equation
where a is not equal to zero.
Let us use completing the square method in this general equation.
By dividing a on both LHS and RHS, we get:
On taking LCM, we get
and
in denominator and numerator respectively.
Let us bring
from left hand side to right hand side.
Here, we are going to assume that
is greater than or equal to zero. Note that it can't be less than 1 because since it is negative, the roots becomes unreal. On taking square roots, we get:
From this we can say that the roots of the quadratic equation are:
This formula for finding the roots of the quadratic equation is called as quadratic formula.
Hence, derived!