What is the meaning of solving a quadratic equation?
Suppose, we have quadratic equation which is in the standard form
. We want to find value of
such that left hand side becomes equal to right hand side which is 0.
For example, we have Quadratic Equation
Putting
in Quadratic Equation, we get left hand side equal to
Therefore, L.H.S = R.H.S. It means
is one of the solutions of the quadratic equation
.
Putting x = 3 in equation, we get left hand side equal to
Therefore, L.H.S = R.H.S. It means
is another solution of the quadratic equation
.
We can here say that
are solutions of the Quadratic Equation
.
Solutions of any Quadratic Equation are also called roots of the Quadratic Equation.
How can we find roots of the Quadratic Equation by Factorization?
Suppose, we are given a Quadratic Equation of the form
where,
.
We can factorize this equation through middle term which is
. We split middle term into two terms in such a way that product of terms becomes equal to
.
For example, we have equation
In this equation, we have
Therefore, we split middle term
into two terms which are
and
because their product is equal to
. Remember that, we also need (
).
Following the process, we can say that
, or
Lets take another example, Find value of
in Quadratic Equation.
We split the middle term into two terms such that their product become equal to
.
If, you cannot figure out directly what are the terms which make product equal to
then start trying different combinations of splitting.
{Product of terms (
and
) is not equal to
}
{Product of terms (
and
) is not equal to
}
{Product of terms (
and
) is not equal to
}
{Product of terms (
and
) is equal to
}, Therefore, we consider this combination.
, or
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