Can you help? Prove that the quadratic equation x^2+bx+c = 0 can be expressed in the form (2x+b)^2 = b^2 - 4c. Thanks?

👨🏻‍🏫 學術台數學

Joanne

2016-06-21 10:32 am

回答 (1)

fooks

2016-06-21 10:36 am

✔ 最佳答案

x² + bx + c = 0
4x² + 4bx + 4c = 0
4x² + 4bx = - 4c
4x² + 4bx + b² = - 4c + b²
(2x)² + 2(2x)(b) + (b)² = b² - 4ac
(2x + b)² = b² - 4ac

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