Which method most efficient method to solve x2+5x-6=0

Factoring is the best method to factor this, as it’s easier and quicker to use. - 6 and 1, when multiplied, get the c value (-6) and when added together get the b value (5). So then you take the opposite of them, 6 and - 1, and that’s your answer.

x=-1 or 6

Short Answer

Factoring for sure.

Discussion

Although if you have a calculator that solves these questions, then that by far is the quickest way. Most teachers won't let you use a calculator however. Or not for something like this. Graphing calculators usually can be programed to to solve this kind of question. A calculator would be nifty to solve a question like the one we've been discussing

y = 6x^2 + 13x - 323

There's no common factors to reduce this and it's going to be hard going to factor it by guess and by golly. In fact it does factor (see below).

The next best thing you can do is use the quadratic formula

x = [-b + / - sqrt (b^2 - 4ac) ]/2a That works and it is not too laborious.

To confirm your answer, you could use something like demos to graph your quadratic. I'll put the two we are discussing on the same graph. They may not be very compatible. We are, after all, just discussing method.

For small simple numbers, just factor by sight.

For small simple numbers, graph

For intermediate numbers use the quadratic formula

For large numbers use the quadratic formula

In all cases try to graph the results. That may save you from even factoring by sight.

Answer for this question

(x + 6) (x - 1) = 0

x + 6 = 0

x = - 6

x - 1 = 0

x = 1

The two solutions are (1,0) and (-6,0) Note that the graph gives you that immediately.

I've added the two graphs separately on their axis. I'm a great believer in graphs. They really do tell a story that is worth 1000 words. Those two are not very compatible. Go to desmos for all graphing questions.