Question

(4) Multiply the given polynomials.
(i) 2x ; x?- 2x - 1 (ii) x-1 ; r3+ 2x2 +2​

Answer 1

Answer:

so, the polynomial factors into, x^2 - 2x - 1 = {x - r+} * {x - r-}. x^2 - 2x - 1 = {x - [1 + sqrt(2)]} * {x - [1 - sqrt(2)]}. Carry out the multiplication and you will find that the two sides of this equation are equal.

2)x

3

−2x

2

+4x+5074=0 (given)

r

1

+r

2

+r

3

=

a

−b

=

1

−(−2)

=2 ---(i)

r

1

r

2

+r

2

r

3

+r

3

r

1

=

a

c

=

1

4

=4 ---(ii)

r

1

r

2

r

3

=

a

−d

=

1

−5074

=−5074 ---(iii)

(r

1

+2)(r

2

+2)(r

3

+2)=(r

1

+2)(r

2

r

3

+2r

2

+2r

3

+4)

=r

1

r

2

r

3

+2r

1

r

2

+2r

3

r

1

+4r

1

+2r

2

r

3

+4r

2

+4r

3

+8

=r

1

r

2

r

3

+2(r

1

r

2

+r

2

r

3

+r

3

r

1

)+4(r

1

+r

2

+r

3

)+8

=−5074+2(4)+4(2)+8 [from (i),(ii) and (iii)]

=−5074+8+8+8

=24−5074

=−505.