Question

Show that

5x+2
3x
+1⁄/12
can be written in the form
ax+b
CX
where a, b and c are integers.

Answer 1

Explanation:

When completing the square, an expression like,

ax2 + bx + c is written in the form (Ax + B)2 + C.

We will begin with the simple example where a = 1. In this case we will write expressions in the form

x2 + bx + c as (x + B)2 + C

If we expand (x + B)2 + C we get x2 + 2Bx + B2 + C.

Comparing this with x2 + bx + c shows that

b = 2B and c = B2 + C

which gives B =

b

2

and C = c – B2