Oxford University Maths Admissions Test 2023 Question 7

University of Oxford Mathematician Dr Tom Crawford answers each Oxford Maths Admissions Test question in under 60 seconds. This is Q7 from the 2023 MAT.

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[lappywong]

Prefer
a^2-4bc
=a^2-64a^2
=-63a^2
<0

[nol]

I took this test and got this one wrong, the steps taken seem so arbitrary when you’re in the moment especially under time pressure it’s hard to come up with that on the spot
The other MCQ were comparatively easier

[alonbenjo]

At the last step:
bc/16 - 4bc = bc (1/16 - 4) which is strictly negative
Why is it negative? We know that b and c are non zero, but maybe one of them is positive and the other one is negative so (1/16-4)bc is now strictly positive

[treush]

I think you’re kinda wrong because you do not Check the sign of bc because you affimated it was positive (obviously positive because of the formulas we have) which is not trivial

[davidworley]

I did this with roots of polynomials and got the same answer but it took 10 minutes 😭

[smayu]

cant we divide the 2 discriminant equations at the start for b^2/c^2 = c/b so b^3=c^3 so b=c?

[ynaf]

How do you make these questions so much easier? I had to substitute cb in the formula to root of 4ba times root of 4ac ending in some kind of infinite successive powers progression, with 4a as a1. As I wanted the multiplication of all the infinite terms I could just add up the infinite powers (which form a geometric progression of ratio 1/2) to then raise 4a and finally find bc is equal to 16a^2.