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AS maths Core Pure Series question

Images and question below
Reply 1
My question is about part b)
2B5CB454-2509-4F33-B22E-D5C1EF2B3174.jpeg
This is the solution
C16F8587-177C-49B9-A080-E39BE24FE921.jpeg

I understood the whole of the solution until the last 2 lines where it talked about the discriminant not being a square. Why would that mean there are no values of n that satisfy blah blah blah(the question)? Is it because the discriminant not being a square would give a decimal (not an integer), hence proving there are no values of n that…(blah blah blah)? But hypothetically even if we had a square number, say 16, that would still give decimal values of n. So why/how does the discriminant not being a square prove the question?
Reply 2
Original post by Sha.xo527
My question is about part b)
2B5CB454-2509-4F33-B22E-D5C1EF2B3174.jpeg
This is the solution
C16F8587-177C-49B9-A080-E39BE24FE921.jpeg

I understood the whole of the solution until the last 2 lines where it talked about the discriminant not being a square. Why would that mean there are no values of n that satisfy blah blah blah(the question)? Is it because the discriminant not being a square would give a decimal (not an integer), hence proving there are no values of n that…(blah blah blah)? But hypothetically even if we had a square number, say 16, that would still give decimal values of n. So why/how does the discriminant not being a square prove the question?


Why not just try it yourself, so what is n using the usual quadratic formula?
If the discriminant is not a square, what does it tell you?
What are the necessary conditions for n to be an integer using the quadratic formula?
(edited 7 months ago)
Reply 3
Original post by mqb2766
Why not just try it yourself, so what is n using the usual quadratic formula?
If the discriminant is not a square, what does it tell you?
What are the necessary conditions for n to be an integer using the quadratic formula?

Just found this after looking at your profile, I appreciate your help. So the necessary conditions for n to be an integer would be 1) square discriminant and 2) the values of the square root of the discriminant, when added or substrates to negative b divided by 2a, must also be rational numbers
(edited 7 months ago)
Reply 4
Original post by Sha.xo527
Just found this after looking at your profile, I appreciate your help. So the necessary conditions for n to be an integer would be 1) square discriminant and 2) the values of the square root of the discriminant, when added or substrates to negative b divided by 2a, must also be rational numbers


Sort of, but to be clear for 2) that
-b +/-sqrt(discriminant)
must be divisble by 2a, so the result is a positive integer/natural number. Itll always be rational when discriminant is square (irrespective of whether its divisble or not), but youre interested in positive integer values, so it must be divisble by 2a. If discriminat is not square, the result is always a surd (integer coefficients). So the test in the model solution is good for this question as it shows n is a surd.

Its good to post your working, rather than just the model solutions. For stuff like this, youre probably expected to do the reasoning yourself rather than simply learn lots of rules, so learning how to make the necessary arguments is part of such questions.
(edited 7 months ago)

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