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# Step II 1999, q2

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1. I've done the question, but I have no idea how many marks I would get because of formality/rigour/correct use of signs etc.

If someone could give me some general guidance & marks out of 20 I would appreciate it hugely. It's just so I don't walk naively into the exam in about 2 months and lose huge marks on silly things, cheers.

Here is a given solution:

i) Where p=3 q=50 r=2 and s=15 find the set of values for n where the equation above has no real roots.

For non-real roots we need
Inserting the given values of p, q, r and s:

Solving for the positive case we have and the negative case
I.e. the equation lacks real roots when and

ii) Prove that if p<r and then the above equation has no real roots fo any n.

Recall from i) that for non-real roots
Solving for n gives and is obviously complex when and thus there are no real solutions for any n.

iii) Find when the above equation has real roots when n=1, (p-r)=1 and
For real roots , and with the above values this transfers to finding where
Solving the positive case gives as desired and the negative case gives as desired.

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