(僅供參考)
(2)
(px - q)(qx + p) = 0
2.
先計算 b^2 - 4ac
= (b - c)^2 - 4(a - b)(c - a)
= 4a^2 + b^2 + c^2 - 4ab + 2bc - 4ac
調整成
= b^2 + c^2 + (-2a)^2 + 2(-2a)b + 2bc + 2(-2a)c
= (b + c - 2a)^2
再套入公式解
x = (c-a)/(a-b) 或 1
3.
α - β = 4
α = 5β
=> α = 5, β = 1
(1) 5, 1
(2) α + β = 6 = 2a => a = 3
4.
x = 0 代入可得
k^2 + 3k + 2 = 0
(k + 1)(k + 2) = 0
k = -1(不合) 或 -2
6.
兩根乘積 α · β = k(4 - k) = -12
k^2 - 4k - 12 = 0
(k - 6)(k + 2) = 0
k = 6 或 -2
α + β = -p = 6 + (-2) = 4
=> p = -4
(2)
(-x + x - k + 2)^2 = 0
-k + 2 = 0
=> k = 2
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