# Explain, please?

1. The coefficient of x^9 in the polynomial (x+1)(x+2)..(x+10)+(x+2)(x+3)..(x+11)+...+(x+11)(x+12)..(x+20) is

a)1551

b)1155

c) 5115

2. Let 1,ω,ω^2 be the cubic roots of unity, then the value of

[(5-3ω/-3+5ω^2)-(3+5ω^2/3ω+5)]^6

3. At some point (a, f(a)) on the graph of f(x) = -1 + 2x - x^2 the tangent to this graph goes through the origin. Which point is it?

a) (0,-1)

b) (1,0), (2,-1)

c) (1,0), (-1,-4)

d) (-1,-4), (2,-1)

### 2 Answers

- PopeLv 76 months ago
One question at a time please. Let me look at problem 3.

The function graph would have this equation:

y = -1 + 2x + x²

y = -(x - 1)²

The curve has vertex (1, 0), so the x-axis is one of the tangent lines. That pares the choices down to (b) or (c).

Clearly the other point of tangency would have to be on the left side of the curve, so that eliminates choice (b).