How do you know what method to use when solving ax^2 + bx + c = 0 ?

The question says I need to decide on an appropiate method to use when solving the following equations. How am I supposed to know what the appropiate method is?

The three methods I know and states I should use are:
- factorise
- complete the square
- use the quadratic formula

Examples of the questions are:

a) x^2 + 5x = 0

b) (x-3)^2 - 25 = 0

c) x^2 + 2x + 1 = 16

d) 6x^2 = x + 2

e) 3x^2 + 5x - 2 = 0

Reply 1

Edycal

Well...you can use the Quadratic formula for any of those equations, but leave it as a last resort since it's considered more time consuming than all the others. Factorization is just solving by using trial and error, shouldn't be too hard and complete the square is quite simple as well. It's up to you to choose unless specified in the question i suppose, cheers.

Reply 2

steve2005

Kash:)

Always look to factorise first if you can't then I would recommend completing the square. Don't worry about the 'appropriate' method , if it works it is OK.

Reply 3

Pheylan

For b I'd complete the square seeing as it's already in that form

Reply 4

Long Haired Teen

Kash:)

Anything that says something along the lines of "give your answer to 3 sf" requires squareroot formula :smile:

Reply 5

steve2005

Long Haired Teen

Anything that says something along the lines of "give your answer to 3 sf" requires squareroot formula :smile:

OR Completion of the square.

Reply 6

Miss Mary

Kash:)

The question is wrongly phrased IMO. It should ask you to decide on the faster method to use, not the most appropiate, as they are all appropiate.

Reply 7

punkyrocker

I used to do this by trial and error, roughly, and if I couldn't manage it I just plugged it into the quadratic formula anyway - it doesn't take long at all and it works either way.

Just think, for example in the form of, (x + a)(x + b)=0, taking your example number (c). The a and b must multiply to make -15, and add to make 2x. i.e, 3 and 5. (x + 5)(x -3) = 0. I used to think if there was no combination of two numbers for which that would work by quick estimation in my head, I'd use a more complicated method like quadratic formula/completing the square.

Sorry if that was rubbish to read! :smile:

Reply 8

jonny23563

Try and factorise first. If that doesn't work, just complete the square. I never bother with the quadratic formula, all you're doing is completing the square, why bother risking making a mistake remembering it?

Reply 9

MikeyW09

Being able to complete the square quickly is a very useful ability in later maths, I'd just advise you to practice this a lot. If you get fast it's only 20 seconds or so from start to finish, whereas you can spend minutes looking for factors.

Reply 10

Flying Tempest

try to factorise then if you can't see them fairly quickly complete the square. unless the coeffs are fractions etc. in which case i tend to use formula for ease. all same. for example try completing the square on ax^2+bx+c and you'll end up with the formula.

Reply 11

thegodofgod

ok, you can use factorisation when you know the factors of the equation. Use completing the square when you canot factorise it. Use quadratic formula if you have a calculator nearby or when 'a' is more than 1., eg. 6x^2 - 5x +2 = 0.

hope that helps

Reply 12

Lifeisnice

Kash:)