With quadratic equations that can be factorised how do we know if the factors should be minus or pluses?

Answer 1

In

ax^2 + bx + c

if the sign of the "c" term is positive, then the factors must be either both pluses or both minuses.

If the sign of the "c" term is negative, the factors must be of opposite sign.

If you are lucky enough that the two factors must be either both pluses or both minuses, you can look at the sign of the "b" term. If it is positive, both factors are pluses. If it is negative, both factors are minuses.

Answer 2

OK,

The most general method for forms x^2+bx+c is to find two numbers p and q so that p*q = c and p+q = b
Then, it factors into (x+p)(x+q) and your roots are -p and -q.

When the coefficient of the x^2 term is not 1, life gets a little more complicated. You can try 'guess and check', but I prefer something called the AC method.

For the AC method, you start by multiplying a times c where a and c are the first and last coefficient. For example, in the quadratic 3x^2 -x -2 you would see that a=3 and c=-2.

Next, just like in the sum and product method, you find two numbers p and q that will multiply to give a times c and add together to give b. In this problem, a times c is -6 so, we need two numbers that multiply to give -6 and add to give -1. So, -3 and 2 are the numbers. What do we do with those? Split b into two pieces. So, 3x^2 - x -2 becomes 3x^2 -3x + 2x -2. Now, use factoring by parts and get 3x(x-1) + 2(x- 1) which becomes
(3x+2)(x-1). And, the great thing about it is that it will work every time if the problem is factorable.

Answer 3

If you double check your answer, you should be able to find any sign errors. The sign by the constant term tells you if they are the same or different (assuming that the sign in front of x^2 is positive, then if the sign in front of the constant is positive then the signs are the same, if the sign in front of the constant is negative, then the signs are different).

Answer 4

Once you graph a quadratic equation, that should be clearly apparent in the coordinates' locations.

Answer 5

We can't factorise them all.
For example .
x*x+4*x+10=0 .

Answer 6

When you factorise, you get and expression similar to
(ax + b) * (cx + d).
You make ax + b = 0, or ax = -b, or x = -b / a.
Just apply the rules of signs...
What is that question?

Answer 7

you don't know since a negative number squared equals the same positive number squared. you have to substitute the answer to see if it is a true solution. i assume you are dealing with real numbers vs complex

Answer 8

Go outside and get some fresh air!

Answer 9

ax^2 + bx + c = 0
(_+_)(_+_)

ax^2 - bx + c = 0
(_-_)(_-_)

ax^2 + bx - c = 0
(_+_)(_-_)

ax^2 - bx - c = 0
(_+_)(_-_)