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.
368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.