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Giải bài tập 6.10 trang 16 SGK Toán 9 tập 2 - Kết nối tri thức

Không cần giải phương trình, hãy xác định các hệ số a, b, c, tính biệt thức (Delta ) và xác định số nghiệm của mỗi phương trình sau: a) (11{x^2} + 13x - 1 = 0); b) (9{x^2} + 42x + 49 = 0); c) ({x^2} - 2x + 3 = 0).

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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Đề bài

Không cần giải phương trình, hãy xác định các hệ số a, b, c, tính biệt thức \(\Delta \) và xác định số nghiệm của mỗi phương trình sau: a) \(11{x^2} + 13x - 1 = 0\); b) \(9{x^2} + 42x + 49 = 0\); c) \({x^2} - 2x + 3 = 0\).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Xét phương trình bậc hai một ẩn \(a{x^2} + bx + c = 0\left( {a \ne 0} \right)\). Tính biệt thức \(\Delta  = {b^2} - 4ac\) + Nếu \(\Delta  > 0\) thì phương trình có hai nghiệm phân biệt: \({x_1} = \frac{{ - b + \sqrt \Delta  }}{{2a}};{x_2} = \frac{{ - b - \sqrt \Delta  }}{{2a}}\). + Nếu \(\Delta  = 0\) thì phương trình có nghiệm kép: \({x_1} = {x_2} = \frac{{ - b}}{{2a}}\). + Nếu \(\Delta  < 0\) thì phương trình vô nghiệm.

Lời giải chi tiết

a) Phương trình \(11{x^2} + 13x - 1 = 0\) có \(a = 11;b = 13;c =  - 1\) và \(\Delta  = {13^2} - 4.11.\left( { - 1} \right) = 213 > 0\) nên phương trình có hai nghiệm phân biệt. b) Phương trình \(9{x^2} + 42x + 49 = 0\) có \(a = 9;b = 42;c = 49\) và \(\Delta  = {42^2} - 4.49.9 = 0\) nên phương trình có nghiệm kép. c) Phương trình \({x^2} - 2x + 3 = 0\) có \(a = 1;b =  - 2;c = 3\) và \(\Delta  = {\left( { - 2} \right)^2} - 4.1.3 =  - 8 < 0\) nên phương trình vô nghiệm.

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