You are Here: Home >< Maths

1. Ok, the question is:

"Given that the equation x^2 + 4x + c =0 has unequal real roots, find the range of possible values for c"

You are given that x^2 + 4x + c = (x+2)^2 -4 +c

The way I would do this question, is look at the equation x^2 + 4x + c =0, so a=1, b=4 and c=c. Substitute that into b^2-4ac>0 to find the answer, because b^2-4ac>0 when there are unequal real roots.

I would do this, getting 16-4ac>0, which then simplifies to 4>c.

HOWEVER,
the mark scheme has this method of doing it:

Ok, so they add 4 and subtract c to both sides in order to get (x+2)^2 = 4-c. After that, they then get to 4-c>0. How on earth do they get to this step from the previous step? Can you please explain?!
I can see that 4-c is on the RHS of the equation, but why is that then an answer for the discriminant. Without substituting a=1, b=4 into b^2-4ac to find the discriminant, how do they suddenly get to the stage where they have 4-c>0 from that equation?

I get that the discrimant, b^2-4ac, must be >0. But how do they get the value of the discriminant to be 4-c by using the previous step of (x+2)^2 = 4-c?

2. If 4-c<0, then if you square root both sides of the equation what do you get? Can you find the square root of a negative number? If 4-c<0 then this implies that which should make you feel a bit uncomfortable, think to yourself of a number that when you square it you get a negative result. Can you think of such a number?

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 6, 2016
The home of Results and Clearing

### 1,134

people online now

### 1,567,000

students helped last year
Today on TSR

### Took GCSEs this summer?

Fill in our short survey for Amazon vouchers!

### University open days

1. University of Buckingham
Thu, 23 Aug '18
2. University of Glasgow
Tue, 28 Aug '18
3. University of Aberdeen
Tue, 28 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams