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標題: quadratic equations in one ubknow [打印本頁]

作者: lovecake 時間: 2011-2-16 06:31 PM 標題: quadratic equations in one ubknow

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作者: Simon 時間: 2011-2-16 06:34 PM

Find sum of roots and products of roots to solve it.

作者: firoazen 時間: 2011-2-16 06:53 PM

Q+R=-b
QR=c
(Q+2)(R+2)=b
Q+R+4=-c

作者: weird_man 時間: 2011-2-16 06:59 PM

Q+R = -b
Q . R = c

(Q+2) + (R+2) = -c
Q+2 +R+2 = -c
Q+R +4 = -c

(Q+2)(R+2) = b
QR +2Q + 2R +4 =b
QR +2(Q+R) +4 = b
c +2 (-b) +4 =b
c-2b+4 = b
c+4 =3b----- (1)
-b +4 = -c
c+4 =b-----(2)
b=0
c=-4

作者: weird_man 時間: 2011-2-16 07:02 PM

checking
Q , R are the roots of the equation
x^2+ (0)x + (-4) = 0
x = 2 or -2
Q=2, R= -2
x^2 + (-4)x + (0) = 0
x = 4 or 0
which x = Q+2 and R+2

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