X2 T02 04 forming polynomials (2011)

Forming Polynomials With The Roots Of Another

Forming Polynomials With The Roots Of Another

roots;with equation an formto,polynomialaofrootstheare , ,,If

Forming Polynomials With The Roots Of Another

roots;with equation an formto,polynomialaofrootstheare , ,,If

,1,1,1 )1(

Forming Polynomials With The Roots Of Another

roots;with equation an formto,polynomialaofrootstheare , ,,If

,1,1,1 )1( y

xx

y 1 substitute and 1let

Forming Polynomials With The Roots Of Another

roots;with equation an formto,polynomialaofrootstheare , ,,If

,1,1,1 )1( y

xx

y 1 substitute and 1let

,,,)2( kkk

Forming Polynomials With The Roots Of Another

roots;with equation an formto,polynomialaofrootstheare , ,,If

,1,1,1 )1( y

xx

y 1 substitute and 1let

,,,)2( kkkkyxkxy substitute and let

Forming Polynomials With The Roots Of Another

roots;with equation an formto,polynomialaofrootstheare , ,,If

,1,1,1 )1( y

xx

y 1 substitute and 1let

,,,)2( kkkkyxkxy substitute and let

,,,c)3( cc

Forming Polynomials With The Roots Of Another

roots;with equation an formto,polynomialaofrootstheare , ,,If

,1,1,1 )1( y

xx

y 1 substitute and 1let

,,,)2( kkkkyxkxy substitute and let

,,,c)3( cc cyxcxy substituteand let

Forming Polynomials With The Roots Of Another

roots;with equation an formto,polynomialaofrootstheare , ,,If

,1,1,1 )1( y

xx

y 1 substitute and 1let

,,,)2( kkkkyxkxy substitute and let

,,,c)3( cc cyxcxy substituteand let

,,, )4( 222

Forming Polynomials With The Roots Of Another

roots;with equation an formto,polynomialaofrootstheare , ,,If

,1,1,1 )1( y

xx

y 1 substitute and 1let

,,,)2( kkkkyxkxy substitute and let

,,,c)3( cc cyxcxy substituteand let

,,, )4( 222 21

2 substitute and let yxxy

e.g.are; roots whose

equation an form ,02 of roots theare ,, If 3 xx

e.g.are; roots whose

equation an form ,02 of roots theare ,, If 3 xx

1,1,1 a)

e.g.are; roots whose

equation an form ,02 of roots theare ,, If 3 xx

1,1,1 a)

yx

xy

1

1let

e.g.are; roots whose

equation an form ,02 of roots theare ,, If 3 xx

1,1,1 a)

yx

xy

1

1let

02113

yy

e.g.are; roots whose

equation an form ,02 of roots theare ,, If 3 xx

1,1,1 a)

yx

xy

1

1let

02113

yy

021 32 yy

11,1,b)

11,1,b)

11let

yxxy

11,1,b)

11let

yxxy 0211 3 yy

11,1,b)

11let

yxxy 0211 3 yy

043021133

23

23

yyyyyyy

11,1,b)

11let

yxxy 0211 3 yy

043021133

23

23

yyyyyyy

222 ,, c)

11,1,b)

11let

yxxy 0211 3 yy

043021133

23

23

yyyyyyy

222 ,, c)

21

2let

yx

xy

11,1,b)

11let

yxxy 0211 3 yy

043021133

23

23

yyyyyyy

222 ,, c)

21

2let

yx

xy

02213

21

yy

11,1,b)

11let

yxxy 0211 3 yy

043021133

23

23

yyyyyyy

222 ,, c)

21

2let

yx

xy

02213

21

yy

0221

23

yy

11,1,b)

11let

yxxy 0211 3 yy

043021133

23

23

yyyyyyy

222 ,, c)

21

2let

yx

xy

02213

21

yy

0221

23

yy

2121

yy

11,1,b)

11let

yxxy 0211 3 yy

043021133

23

23

yyyyyyy

222 ,, c)

21

2let

yx

xy

02213

21

yy

0221

23

yy

2121

yy

41 2 yy

11,1,b)

11let

yxxy 0211 3 yy

043021133

23

23

yyyyyyy

222 ,, c)

21

2let

yx

xy

02213

21

yy

0221

23

yy

2121

yy

41 2 yy

04242

23

23

yyyyyy

2221,1,1 d)

2221,1,1 d)

21

21let

yx

xy

2221,1,1 d)

21

21let

yx

xy 022

123

yy

2221,1,1 d)

21

21let

yx

xy 022

123

yy

2123

yy

2221,1,1 d)

21

21let

yx

xy 022

123

yy

2123

yy

23

21 yy

2221,1,1 d)

21

21let

yx

xy 022

123

yy

2123

yy

32 41 yy

23

21 yy

2221,1,1 d)

21

21let

yx

xy 022

123

yy

2123

yy

32 41 yy

0124412

23

32

yyyyyy

23

21 yy

222 Find e)

222 Find e)

22

222

222 Find e)

22

222

2

120 2

222 Find e)

22

222

2

120 2

OR using equation found in c)

222 Find e)

22

222

2

120 2

OR using equation found in c)

ab

222

222 Find e)

22

222

2

120 2

OR using equation found in c)

ab

222

212

222 Find e)

22

222

2

120 2

OR using equation found in c)

ab

222

212

Exercise 5D; 10 to 16

Exercise 5E; 2cd, 4b, 7, 9, 10, 18, 27, 30, 34, 35