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# AQA C1 Inequalties help Watch

1. I was doing the June 2013 AQA C1 paper and I'm stuck on question 7a), I work it out as b^2 - 4ac > 0 for real roots however they answer wants the > to have a line underneath it, I reverse the symbol and get the answer however, I do not know when / why I need to put a line under the <.

I have attached the question and mark scheme thanks

Btw my working is:
real roots when b^2 - 4ac > 0
[-(k-2)]^2 - 4 x (2k-7) x (k-3) > 0
(-k+2)^2 - (8k+28)(k-3) > 0
k^2 - 4k +4 - (8k^2 - 24k - 28k + 84) > 0
k^2 - 4k + 4 -8k^2 + 52k - 84 >0
-7k^2 + 48k -80 >0
7k^2 - 48k +80 < 0
therefore shown
Attached Images

2. You can also have a single real, repeated root when the discriminant is 0
3. (Original post by Sayless)
real roots when b^2 - 4ac > 0
If the discriminant is:
then the roots are real and distinct - i.e. two of them.
then there is one real root (repeated).
there are two complex roots.

So, if you require the roots to be real, then the discriminant must be positive or it must be zero.

4. (Original post by ghostwalker)
If the discriminant is:
then the roots are real and distinct - i.e. two of them.
then there is one real root (repeated).
there are two complex roots.

So, if you require the roots to be real, then the discriminant must be positive or it must be zero.

So only real roots at = 0 and >0 and > with a line underneath means both of = and > therefore thats why it was used, thanks for the help
5. (Original post by Sayless)
So only real roots at = 0 and >0 and > with a line underneath means both of = and > therefore thats why it was used, thanks for the help
Just to be clear > with a line underneath is read as "greater than or equal to"

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