TMUA Euclid Sample Paper 1 · Question 18

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Euclid Sample Paper 1 · Q18

Paper 1CalculusGeometryAlgebra

A quartic polynomial $P$ has leading coefficient $4$ and satisfies

P(x)\geq0

for every real $x$ . It has exactly two distinct real roots and also satisfies

P(1)=P(-1)\qquad\text{and}\qquad P(2)-P(-2)=192.

The three stationary points of the curve $y=P(x)$ form a triangle. What is the area of this triangle?

8

8\sqrt2

16

16\sqrt2

24

24\sqrt2

32

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