The profit functions for two competing electronics startups are modeled by P(x)=2x2+ax+bP(x) = 2x^2 + ax + bP(x)=2x2+ax+b and Q(x)=2x2+cx+dQ(x) = 2x^2 + cx + dQ(x)=2x2+cx+d, where xxx represents the number of units sold (in thousands). It is discovered that both startups break even at exactly the same positive production level, specifically when (2x−9)(2x - 9)(2x−9) is a factor of both profit functions.
Show that 9(c−a)=2(b−d)9(c - a) = 2(b - d)9(c−a)=2(b−d).
Fully justify your answer.
306 exam-style questions on CCEA A Level Maths 1.1 Algebra and functions, covering 1.1.1 Algebra and functions, 1.1.2 Algebra and functions, 1.1.3 Algebra and functions, 1.1.4 Algebra and functions, 1.1.5 Algebra and functions, 1.1.6 Algebra and functions, 1.1.7 Algebra and functions, 1.1.8 Algebra and functions, 1.1.9 Algebra and functions, 1.1.10 Algebra and functions, 1.1.11 Algebra and functions, 1.1.12 Algebra and functions, 1.1.13 Algebra and functions, and 1.1.14 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.