Cho đa thức F(x) = 2ax2 + bx (a,b là hằng số). Xác định a,b để đa thức F(x) có nghiệm x = -1 và F(1) = 4

Vì đa thức F(x) có nghiệm x = -1 nên thay F(-1) = 0

⇒ 2a - b = 0 ⇒ b = 2a (0.5 điểm)

Vì F(1) = 4 ⇒ 2a + b = 4 ⇒ b = 4 - 2a

Từ đây ta có 2a = 4 - 2a ⇒ 4a = 4 ⇒ a = 1 (0.5 điểm)

Vì x = -1 là nghiệm của H(x) nên

H(-1) = 0 ⇒ 2a(-1)2 + b(-1) = 2a - b = 0 ⇒ b = 2a

Vì H(1) = 4 ⇒ 2a.12 + b.1 = 2a + b = 4 ⇒ b = 4 - 2a

Ta có 2a = 4 - 2a ⇒ 4a = 4 ⇒ a = 1, từ đó b = 2. Chọn B

1 C

2 C

3 B

4 C

5 C

6 D

F(1)=G(-1)

=>3+2a+a-5=1-3a-4

=>3a-2=-3a-3

=>6a=-1

=>a=-1/6

Thay x= - 1 vào đa thức , ta có

F(x)= 2a(-1)² + b(-1)

F(x)= 2a-b

Đặt F(x)=0, ta có :

2a-b=0=> 2a = b hay b gấp đôi a

ccmnr

Ta có ax^3 + by^3 = (x + y)(ax^2 + by^2) - xy(ax + by) => 9 = 5(x + y) - 3xy (1) ax^4 + by^4 = (x + y)(ax^3 + by^3) - xy(ax^2 + by^2) => 17 = 9(x + y) - 5xy (2) Từ (1) và (2) => x + y = 3 và xy = 2 => x, y là nghiệm của pt ∝^2 - 3∝ + 2 = 0 (∝ - 1)(∝ - 2) = 0 ∝ = 1 hoặc ∝ = 2 => (x , y) = (1 ; 2) hoặc (2 ; 1) Không mất tính tổng quát, giả sử (x , y) = (1 ; 2) Giả thiết ban đầu a + 2b = 3; a + 4b = 5 ; a + 8b = 9 ; a + 16b = 17 => a = b = 1 Vậy ax^2001 + by^2001 = 1.1^2001 + 1.2^2001 = 1 + 2^2001

Ta có ax^3 + by^3 = (x + y)(ax^2 + by^2) - xy(ax + by) => 9 = 5(x + y) - 3xy (1) ax^4 + by^4 = (x + y)(ax^3 + by^3) - xy(ax^2 + by^2) => 17 = 9(x + y) - 5xy (2) Từ (1) và (2) => x + y = 3 và xy = 2 => x, y là nghiệm của pt ∝^2 - 3∝ + 2 = 0 (∝ - 1)(∝ - 2) = 0 ∝ = 1 hoặc ∝ = 2 => (x , y) = (1 ; 2) hoặc (2 ; 1) Không mất tính tổng quát, giả sử (x , y) = (1 ; 2) Giả thiết ban đầu a + 2b = 3; a + 4b = 5 ; a + 8b = 9 ; a + 16b = 17 => a = b = 1 Vậy ax^2001 + by^2001 = 1.1^2001 + 1.2^2001 = 1 + 2^2001

. Choose the best answer A, B, C or D to complete the sentences:

1. My house isn’t very far _________school, so I usually go to school _________ bike.

A. from- on          B. away - in          C. of - by              D. from - by

2. When I was a child, I usually _________fishing with my brother.

A. go                              B. went                 C. gone                 D. used to go

3. They are not _________to take part in this program of the World Health Organization.

A. so old              B. old enough       C. enough old       D. as old

4. Can you turn _________ the TV? I want to see the film.

A. on                    B. off                    C. for                    D. in

5. Peter doesn’t like scuba-diving. _________does his brother.

A. Too                  B. Neither             C. So                    D. Either

6. The football match was postponed _________the bad weather.

A. despite             B. in spite             C. because            D. because of

7. This newspaper _________ every day. It’s a daily newspaper.

A. is publishing     B. is published              C. publishes         D. publish

8. Linda has many _________at school because she is very helpful.

A. friends             B. friendliness      C. friendly            D. unfriendly

9. What is ___thing in one’s life?

A. the most important B. more important than   C. important as    D. important than

10. I felt quite _______ with my day’s work.

A. satisfy              B. satisfactory      C. satisfied           D. satisfaction

1. Super car will …………. water in the future.

A. go by          B. run at                 C. run on     D. travel by

2.  ………  draw on the walls and tables, please.

A. Do               B. Don’t                C. Should    D. Shouldn’t

3.A person who acts in a comedy is a……………  .

      A. comedy        B. comedian C. newsreader               D. producer

4. I………. to Singapore three times.

A. have gone   B. have went          C.went         D.visited

5. We’d like some rice………. lunch.

A. toB.in      C. for D. at

6.  My brother can’t swim ………he’s afraid of water .

 because                 B. but          C. and                              D. so

7. There aren’t  ………  good films on TV at the moment.

     A. some             B. any         C. much                 D. a lot

8.They have been in love with each other ………. they were young.

   A.while                         B. until         C. for                     D. since

9. They think Da Lat is the ……..interesting place they have visited.
A. more	B. better	C. most	D. best
10. It is very unsafe to swim here. The water is heavily………..
A. pollute	B. polluted	C.     polluting	D. pollution

II. Choose the best word or phrase (A, B, C or D) to complete each sentence below (2points)

1. Super car will …………. water in the future.

A. go by          B. run at                 C. run on     D. travel by

2.  ………  draw on the walls and tables, please.

A. Do               B. Don’t                C. Should    D. Shouldn’t

3.A person who acts in a comedy is a……………  .

      A. comedy        B. comedian C. newsreader               D. producer

4. I………. to Singapore three times.

A. have gone   B. have went          C.went         D.visited

5. We’d like some rice………. lunch.

A. toB.in      C. for D. at

6.  My brother can’t swim ………he’s afraid of water .

 because                 B. but          C. and                              D. so

7. There aren’t  ………  good films on TV at the moment.

     A. some             B. any         C. much                 D. a lot

8.They have been in love with each other ………. they were young.

   A.while                         B. until         C. for                     D. since

9. They think Da Lat is the ……..interesting place they have visited.
A. more	B. better	C. most	D. best
10. It is very unsafe to swim here. The water is heavily………..
A. pollute	B. polluted	C.     polluting	D. pollution

 

1. Super car will …………. water in the future.

A. go by          B. run at                 C. run on     D. travel by

2.  ………  draw on the walls and tables, please.

A. Do               B. Don’t                C. Should    D. Shouldn’t

3.A person who acts in a comedy is a……………  .

      A. comedy        B. comedian C. newsreader               D. producer

4. I………. to Singapore three times.

A. have gone   B. have went          C.went         D.visited

5. We’d like some rice………. lunch.

A. toB.in      C. for D. at

6.  My brother can’t swim ………he’s afraid of water .

 because                 B. but          C. and                              D. so

7. There aren’t  ………  good films on TV at the moment.

     A. some             B. any         C. much                 D. a lot

8.They have been in love with each other ………. they were young.

   A.while                         B. until         C. for                     D. since

9. They think Da Lat is the ……..interesting place they have visited.
A. more	B. better	C. most	D. best
10. It is very unsafe to swim here. The water is heavily………..
A. pollute	B. polluted	C.     polluting	D. pollution