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Giải mục V trang 51, 52 SGK Toán 7 tập 2 - Cánh diều

a) Tính giá trị của biểu thức đại số

♒Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Cánh diều

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V. Nghiệm của đa thức một biến

HĐ 7

a) Tính giá trị của biểu thức đại số \(3x - 2\) tại x = 2.

b) Tính giá trị của đa thức P(x) = \( - 4x + 6\) tại x = – 3.

Phương pháp giải:

Thay các giá trị của x vào biểu thức, đa thức rồi thực hiện phép tính.

Lời giải chi tiết:

a) Tại xꦐ = 2, giá trị của biểu thức đại số \(3x - 2\)= \(3.2 - 2 = 6 - 2 = 4\).

b) Tại x = – 3, giá trị của đa thức P(x) = \( - 4x + 6\) bằng:

\(P( - 3) =  - 4. - 3 + 6 = 12 + 6 = 18\).

HĐ 8

Cho đa thức \(P(x) = {x^2} - 3x + 2\). Tính P(1), P(2).

Phương pháp giải:

Thay các giá trị của x vào đa thức rồi thực hiện phép tính.

Lời giải chi tiết:

\(P(1) = {1^2} - 3.1 + 2 = 1 - 3 + 2 = 0\). \(P(2) = {2^2} - 3.2 + 2 = 4 - 6 + 2 = 0\).

LT - VD 6

Trong các phát biểu sau, phát biểu nào đúng, phát biểu nào sai?

a) x = 4 và x✤ = – 4 là nghiệm của đa thức\(P(x) = {x^2} - 16\).

b) yꦬ = – 2 là nghiệm của đa thức \(Q(y) =  - 2{y^3} + 4\).

Phương pháp giải:

Muốn kiểm tra phát biểu nào đúng, phát biểu nào sai; ta thay các giá trị x, y vào 2 đa thức đã cho để kiểm tra.

Một giá trị là nghiệm của đa thức khi và chỉ khi giá trị đó khi thay vào đa thức làm cho giá trị của đa thức bằng 0.

Lời giải chi tiết:

a) \(P(4) = {4^2} - 16 = 16 - 16 = 0\).       \(P( - 4) = {( - 4)^2} - 16 = 16 - 16 = 0\).

Vậy x = 4 và x🎶 = – 4 là nghiệm của đa thức \(P(x) = {x^2} - 16\). Phát biểu a) đúng.

b) \(Q( - 2) =  - 2.{( - 2)^3} + 4 =  - 2. (- 8) + 4 = 16 + 4 = 20 \ne 0\).

Vậy y♍ = – 2 không là nghiệm của đa thức \(Q(y) =  - 2{y^3} + 4\). Phát biểu b) sai.

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