when solving quadratic equations, how do you know what method to use?

Question

for example when a question says prove that this equation equals zero would you use the quadratic equation or would you solve it by completing the square or by factorising? Anyone who can help me? I would be very grateful!!! Thanks x

Answer 1

I tend to use either eyeballing or the quadratic equation. I mean if you have something like x^2 - 2x - 24 you can look at it and see that this is (x - 6)(x + 4).

If I can't just see the roots in about 10 seconds, I use the quadratic eqution.

I don't like completing the square, because I think there's too much potential to be working with weird fractions. With the quadratic equation, you don't have to deal with that sort of stuff until the very end. But it's been about twenty-five years since I was taught all this stuff, and we were never taught to complete the square, so maybe I'm just unfamiliar with it.

Answer 2

If I feel that I can factorize on inspection, I do so. I rarely factorize if the coefficient of x^2 is not unity. If it takes me more than a few moments, or I can see upon inspection that it would be difficult (especially if the coefficients are not integers), I go to the quadratic formula.

I vaguely recall learning how to complete the square, but I never use it to solve quadratic equations.

Answer 3

The quadratic equation will always work, but one needs to look at the equation and decide whether to factor, complete the square, etc.

Experience will give one the insight as to which method is easiest to use.
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Answer 4

Only practice can tell you what method is the quickest--but both of the methods you just mentioned will always work.

Answer 5

Practice and experience are your answer. I have to sound like a mother, but do the math.