Year 11 Ext1 Questions (1 Viewer)

[MattMawby]

Hey guys,

A friend from another school gave me a set of questions, and I have done all but four. I was wondering if anybody could solve these questions and let me know how you got them? I would be so appreciative if anybody could do this.

thank you very much!

 

[vds700]

Hey guys,

A friend from another school gave me a set of questions, and I have done all but four. I was wondering if anybody could solve these questions and let me know how you got them? I would be so appreciative if anybody could do this.

thank you very much!

ill do 3.
cos2x = cosx
cos2x - cosx = 0
2cos^2 x - cosx - 1 = 0
(2cosx + 1)(cosx - 1) = 0
cosx = -1/2 or cosx = 1

You should be right to use the fomula for general slution, sorry i cant remember it and im too lazy to look it up.

Hope that helped.

 

[lyounamu]

4. Since it is a monic polynomial, the coefficient of x^3 is 1.

So let's assume the polynomial being P(x) = x^3 + ax^2 + bx - 4

When x = -1, P(-1) = 0
i.e. -1 + a - b - 4 = 0
a - b -5 = 0
a - b = 5
a = 5+b

So the P(x) = x^3 + (5+b)x^2 + bx - 4

 

[solomarc20]

I'll try 1. but am not entirely sure it's correct

Q(x)= (x^2-1)A(x) + R(x)
Q(x)= (x+1)(x-1) A(x) + 5x-2

By the Remainder theorem

Q(-1) = (-1+1)(-1-1)A(-1) + 5(-1)-2
= -7

U'll need 2 double check this...

 

[shadyhaze]

ill do 3.
cos2x = cosx
cos2x - cosx = 0
2cos^2 x - cosx - 1 = 0
(2cosx + 1)(cosx - 1) = 0
cosx = -1/2 or cosx = 1

You should be right to use the fomula for general slution, sorry i cant remember it and im too lazy to look it up.

Hope that helped.

x = 2n(pi)
x = 2n(pi) +- 2(pi)/3