Can you use the quadratic formula instead of factoring

But that's simply not always the case, which is why it's nice that the quadratic formula provides a quick, general solution just in case the expressions aren't nice enough - which is something we can't say for all polynomials!

In short - use whichever method you choose, both are valid. But always be cognizant of the time it takes for you to get the solution any one way, as opposed to another way. No sense in wasting time and energy when the end result is the same. Unless the factorization is obvious e. But looking closely, it is just a way to re-establish the quadratic formula.

There can be an obvious solution, and you are just in the case of factorization "at a glance". In the general case, analytical resolution of this system brings you back to… the quadratic formula. In fact, they are equivalent so it does not matter. Sign up to join this community. The best answers are voted up and rise to the top.

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Learn more. Ask Question. Asked 2 years, 7 months ago. Active 2 years, 7 months ago. Viewed 2k times. Take this for a problem I didn't make it myself I know that the quadratic formula is required to solve the answer, but why not factor?

I previously asked this on Math Overflow, but this is the right place. Thanks in advance. Eevee Trainer This is actually a very good question, but not one with a really definitive answer. The following is mostly some rules of thumb. If the quadratic looks particularly " ugly " use the quadratic formula. Quadratics with coefficients that involve roots would be one example of "ugly". After that if the "ugly" rule doesn't apply : Factoring is usually faster and less prone to arithmetic mistakes if you are working by hand.

Viewed 3k times. This approach helps in understanding, among others, what it means for a polynomial to have a multiple root. Add a comment. Active Oldest Votes. Of course, this method can be refined and made more efficient, but it still needs you to factorize the given polynomial expression.

Determining the type of a singularity. Simplyfing expressions. Uses of this are very wide types of singularties of a function, calculating the limit of a sequence, haveing a "nicer" expression to differentiate Hirshy Hirshy 4, 2 2 gold badges 18 18 silver badges 46 46 bronze badges. Sure if one only talks about solving equations there is no need to factorize expect for less time if you can immediately see the solution.

Max Payne Max Payne 3, 2 2 gold badges 14 14 silver badges 33 33 bronze badges. Mick Mick By solvable , I mean those equations that have real solution. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.