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First take the general form of a quadratic equation, ax^2+bx+c=0, this can be written in completed square form, (x+b/2a)^2-(b/2a)^2+c/a=0, rearranging gives, x=-b/2a +/-(b^2/4a^2-c/a)^1/2, which can be wr...

(a) (i) Use the Factor Theorem to show that x + 3 is a factor of p(x).

The Factor Theorem is derived from the remainder theorem. We know from the remainder theorem that by doing p(x)/(x – a) then w...

There are two different methods of solving this equation and it is important to find the method that you find easiest.

The first method is to split up the numbers and the letters on both sides of t...

When approaching intersection problems, it is important to have both equations and solve them by substituting one into the other or simultaneously. First we need to find the equation of the line l since w...

A. t=0 ; x=250,000 B. 2020, so t=3. plug in to equation > x=250,000e^(0.012)3 = 259,163 (people so cannot round up) C. Population to double so 500,000 = 250,000e^(0.012)t -> 1/0.012(ln2) = t t= 57.7...