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sherendyak
@sherendyak
July 2022
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При каких значениях параметра p уравнение x^2-2(p-1)x+4p^2=0 имеет только один корень? (фото)
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IrkaShevko
Verified answer
X² - 2(p - 1)x + 4p² = 0
имеет один корень, если D = 0
D = 4(p² - 2p + 1) - 16p² = -12p² - 8p + 4 = 0
-3p² - 2p + 1 = 0
D₁ = 4 + 12 = 16
p₁ = (2 - 4)/(-6) = 1/3
p₂ = (2 + 4)/(-6) = -1
Ответ: при p = -1 и p = 1/3
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Answers & Comments
Verified answer
X² - 2(p - 1)x + 4p² = 0имеет один корень, если D = 0
D = 4(p² - 2p + 1) - 16p² = -12p² - 8p + 4 = 0
-3p² - 2p + 1 = 0
D₁ = 4 + 12 = 16
p₁ = (2 - 4)/(-6) = 1/3
p₂ = (2 + 4)/(-6) = -1
Ответ: при p = -1 и p = 1/3