AS/A2 Pure 1 Pure 2

P3 Topic 1: Algebra
Rational functions 5
The display shows the above curve for a=3, b=7, c=1, d=2. Also shown are two red horizontal lines. The curve does not lie between these lines. In other words, y cannot take values between those indicated by the red lines, so y cannot take values between 1 and 9. What values of a, b, c and d make the red lines vanish?

Summary The red lines will vanish when a2cd+b2-ab(c+d) < 0. For example if you keep a=3, c=1, d=2, then b2-9b +18< 0 or (b-6)(b-3) < 0, which happens when b is between 3 and 6. Based on free Java applets from JavaMath