1. a and b are the roots of the quadratic equation
x^2+(p-2)x+p = 0
where p is a real.
(a) Express (a+b) and (ab) in terms of p
(b) If a and b are real such that a^2+b^2 = 11, find the values of p.
F.4 A Maths Q.Equation
2007-10-09 1:15 am
回答 (2)
2007-10-09 1:32 am
✔ 最佳答案
1a) a+b = 2-pab = p
1b a^2 + b^2 = (a+b)^2 - 2ab
2-4p-p^2 - 2p = 11
2-6p-p^2 = 11
9 - 6p p^2 = 0
(p-3)(p-3) = 0
p = 3
參考: me
2007-10-09 1:22 am
(a) a + b = -(p-2) = 2 - p
ab = p
(b) a^2 + b^2 =11
a^2 + 2ab + b^2 = 11 + 2ab
(a + b)^2 = 11 + 2ab
(2 - p)^2 = 11 + 2p
p^2 - 4p + 4 = 11 +2p
p^2 - 6p - 7 = 0
(p - 7)(p + 1) = 0
p = -1 or 7
ab = p
(b) a^2 + b^2 =11
a^2 + 2ab + b^2 = 11 + 2ab
(a + b)^2 = 11 + 2ab
(2 - p)^2 = 11 + 2p
p^2 - 4p + 4 = 11 +2p
p^2 - 6p - 7 = 0
(p - 7)(p + 1) = 0
p = -1 or 7
收錄日期: 2021-04-13 18:45:06
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