Теорема Виета.
Пусть x1 и x2 – корни уравнения x2 + px + q = 0,
тогда x1 + x2 = –p, x1 ⋅ x2 = q.
Замечание. Если дискриминант уравнения равен нулю, то считается, что уравнение имеет два одинаковых корня.
x2 + px + q = 0
x1, x2
x1 + x2
x1 ⋅ x2
x2 + x – 2 = 0
x1 = –2, x2 = 1
x1 + x2 = –2 + 1 = –1
x1 ⋅ x2 = –2 ⋅ 1 = –2
x2 – 9 = 0
x1 = –3, x2 = 3
x1 + x2 = –3 + 3 = 0
x1 ⋅ x2 = –3 ⋅ 3 = –9
x2 – 4x + 4 = 0
x1 = 2, x2 = 2
x1 + x2 = 2 + 2 = 4
x1 ⋅ x2 = 2 ⋅ 2 = 4
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