3.The quadratic equation 9x2 – (k+1)x + 1 = 0 has equal roots.
(a)Express the discriminant of the equation in terms of k.
(b)Hence, find the two possible values of k.
(c)If k takes the negative value obtained in (b), solve the given equation.
help! F.4 maths
2009-10-11 8:24 pm
回答 (1)
2009-10-11 10:11 pm
✔ 最佳答案
9x2 - (k + 1)x + 1 = 0 has equal roots.a. Discriminant
= [-(k + 1)]2 - 4(9)(1)
= (k + 1)2 - 36
b. For the equation has equal roots, discriminant = 0
(k + 1)2 - 36 = 0
(k + 1)2 = 36
k + 1 = 6 or -6
k = 5 or -7
c. k = -7,
The equation becomes:
9x2 - (-7 + 1)x + 1 = 0
9x2 + 6x + 1 = 0
(3x + 1)2 = 0
x = -1/3 (repeated)
參考: Physics king
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