math mc

2009-09-05 1:44 am
how many distinct real roots does the eequation X^4+7x^2-8=0 have ?

A.1
B.2
C.3
D.4


想問點解係2個real roots?

回答 (1)

2009-09-05 1:59 am
✔ 最佳答案
The answer is : B. 2

x4 + 7x2 - 8 = 0
(x2)2 + 7(x2) + 8 = 0
(x2 + 8)(x2 - 1) = 0
x2 + 8 = 0 or x2 - 1 = 0

When x2 + 8 = 0:
a = 1, b = 0, c = 8
Discriminant Δ
= (0)2 - 4(1)(8)
= -32 < 0
Hence, there is no real roots for x2 + 8 = 0

When x2 - 1 = 0:
a = 1, b = 0, c = -1
Discriminant Δ
= (0)2 - 4(1)(-1)
= 4 > 0
Hence, there are 2 real roots for x2 - 1 = 0

Total number of real roots
= 0 + 2
= 2


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