Question

what adds 4 and multiplies to -3?

Answer 1

anyone know??

Answer 2

you mean like, two numbers that add up to 4 and multiply to -3?

Answer 3

yes

Answer 4

i don't think it's possible

Answer 5

thats what i thought the equation is y=-x2+4x-3

Answer 6

2±√7 ?

Answer 7

i got the vertex i need to find the intercepts

Answer 8

Ah, if the x^2 is negative, you can multiply through by a -1 to change the signs.

Answer 9

Now you can use rational numbers - now the question is, what adds to -4 and multiplies to +3?

Answer 10

why is it reversed now?

Answer 11

The x^2 term was negative; you need to factor that out before factoring the trinomial as a whole.

Answer 12

the two isnt negative there's a -1 in front of the x^2

Answer 13

That's correct. That's what I said.

Answer 14

unless do i set it to -x^2+4x-3=0?

Answer 15

It's the same thing. Ultimately, if you are trying to find x-intercepts, then you set the polynomial to zero, and since your leading coefficient is -1, it's easiest to multiply both sides of the equation by -1 to make it positive, then you can use the factoring shortcut.

Answer 16

but then what are the two numbers? i cant even get it?

Answer 17

3 is a prime number, it only has 2 factors.

Answer 18

then its x-3, x-1 but i still dont know why the signs get reversed

Answer 19

Here is how to do it without reversing the signs.
Given -x^2+4x-3 and you want to factor it without factoring out the -1 first:
You first multiply -1 by -3 to get 3. Factors of 3 that add to 4 are 1 and 3.
Now split the middle term using those factors:
-x^2 +x +3x -3.
Now do factoring-by-grouping:
x(-x+1) -3(-x+1) = (x-3)(-x+1).
Still free to factor out the -1 and get -(x-3)(x-1).

Personally, I'd rather not go to that trouble if I didn't have to; I'd just factor out the -1 immediately and dispose of it because it doesn't change what the x-intercepts are.