I've been trying to factorise the following equation:
4p^2 + 12p + 9 = 0
I can't seem to find any values for a and b so that 4a+b=12 and a*b=9
Any help on this?
I find that explaining methods of factoring is very tricky... basically I take advantage of the fact that I had it drilled into me and I am quite quick with multiplying in my head
But here's my shot at it
4 has the following factors 1,2,2,4
So if this thing is factorable it has one of the two forms below
1) (x )(4x ) or
2) (2x )(2x )
So I just pick one and run with it, let's say we guess wrong
Try (x )(4x )
Now 9 has the factors 1,3,3,9 so we can put 1,9 together in any order or 3,3 together
Since 9 is positive, either both numbers are negative or both numbers are positive
So our possible combinations are: (x+3)(4x+3), (x-3)(4x-3), (x+1)(4x+9), (x+9)(4x+1), (x-1)(4x-9), (x-9)(4x-1)
I run through all these in my head and realize that I was not getting 12x out of the deal, so I move to the next one
Try (2x )(2x )
Now for blank space we have exactly the same combinations as above, I run through them in my head (and by this I mean I say to myself (2x+1)(2x+9) will give me 20x, nope no good try again)
and I get that (2x+3)(2x+3) is my answer
hope this helps
and by the way, this method is significantly quicker than setting up those equations and looking at it once you get good with this
Ok, I kind of understand it. I also used the quadratic formula and got -3/2 which makes sense:
(x+3/2)(x+3/2) /// multiplied by 2
So in this case there's only one solution: x=-3/2
I'll need to practise it a lot more. I am ok when the coefficient 'a' is 1 as in x^2+4x........ but when 'a' is different to 1 then I sometimes struggle.
you can of course always apply the quadratic formula
When you apply it, you get 2 answers in general, call them and
Then the quadratic can be written as
In your case
So if you were stuck on a test and had time this is a fail safe, but obviously factoring is preferred
This is how your work should work:
Therefore is .
P cannot equal -3 over 2. The root is -3 over 2.