Kenneth S. answered • 01/23/17
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YES, the quadratic formula should be used, if easier methods (eg factoring) do not apply.
if the discriminant is negative, of course then you will be obtaining complex number results, based on i2 = -1.
Kenneth S.
It's not a question of reliability (the quadratic formula is infallible). But the practical fact is that when people complete the square, they are in a sense reinventing the wheel, because the quadratic formula was developed by completing the square. Completing the square is a process that, I have observed, is more error prone for many students, especially when the coefficient of the squared term is other than 1).
As a general rule, factor if you can--otherwise revert to using quadratic formula. But be prepared to use completion of the square in special instances such as putting equations of conics into standard form.
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01/24/17
Aniya W.
Thank you very much for your help!! I was confused at first because I thought the quadratic formula was only used to solve certain types of equations like factoring.
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01/24/17
Kenneth S.
You are welcome, Aniya. Here's a useful fact not often conveyed in the standard curriculum: if a quadratic is factorable, then the discriminant must be a perfect square (e.g. 4, 16, 25, 121, etc.).
Why? because, if the discriminant is not a perfect square, then the quadratic formula gives the two solutions, each of which involves an IRRATIONAL part.
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01/24/17
Aniya W.
01/24/17