Can every quadratic equation be solved by factorization or by splitting the middle term? When does one use quadratic formula?
1 Answer
No. Every quadratic equation has two solutions and can be factorized, but as level of difficulty rises, splitting may not be easy and one may tend to use quadratic formula.
Explanation:
According to fundamental theorem of algebra, a polynomial of degree
To factorize a quadratic polynomial of general form
Assume factors of
So one splits
However, splitting of numbers this way may not be easy. For example though
it may not be easy far every one to factorize
Generally, it is easier only when roots of the quadratic equation are rational numbers. This happens when the
When we switch to irrational numbers or complex numbers, complexities grow and as according to fundamental theorem of algebra a quadratic equation has two roots, one can use quadratic formula. For example, using quadratic formula the factors of
Thus
Hence, every quadratic equation has two solutions and can be factorized, but as level of difficulty rises, splitting may not be easy and one may tend to use quadratic formula.