Euations

👨🏻‍🏫 學術台數學

Cham

2007-04-05 11:45 pm

If the roots of the equation x^2-2(a-1)x-(b+2)=0 are equal,find
A) a^999+b^3;
B) a quadratic equation with roots a and b

更新1:

Hello mungks, Your answer is not the same as the ansewer. Can you please look at it again?

回答 (1)

阿爺

2007-04-06 6:46 pm

✔ 最佳答案

If the roots are equal, then
4(a-1)^2 + 4(b+2) = 0
b = -2 - (a-1)^2

A) a^999+b^3
= a^999 + [-2 - (a-1)^2]
= a^999 - (a^2-2a+3)^3
= a^999 -a^6 +6a^5-21a^4+44a^3-63a^2+54a-27

B) the quatratic equation with roots a and b :
(x-a)(x-b)=0
x^2-(a+b)x+ab=0
x^2 + (a^2-3a+3)x -a(a^2-2a+3)=0

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