TMUA 2020 Paper 2 Q18 — Worked Solution

P2·Algebra & Surds, Logic & Quantifiers·7.0Official · 2020 · Q18

cubic-polynomialspositive-for-all-xmust-be-true

In this question,

f (x) = a x^{3} + b x^{2} + c x + d

and

g (x) = p x^{3} + q x^{2} + r x + s

are cubic polynomials.Suppose

f (x) - g (x) > 0

for every real

x

.Which of the following is/are necessarily true?

a > p

b = q

then

c = r

III

d > s

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