f4 quadratic equation

yan

2009-10-13 1:34 am

1. If n<0, which of the following about the roots of the quadratic equation (x+m)^2=-n is correct?
A. x= +-√n
B. x= -m+-√(-n)
C. x= m+-√(-n)
D. x= -m+-√(-n)

2.If x^2+12x+m^2 can be written as a perfect square, then m=
A. 6
B. +-6
C. 36
D. +-36

3.Which of the following equations has/have one double real root?
I. 5x^2=0
II. x^2-5^2=0
III.(x-5)^2=0
A.I only
B.II only
C.I and III only
D. II and III only

4. If a+b-c=0, then which of the folowing euations has 1 as a root?
A. ax^2+bx+c=0
B. ax^2-bx-c=0
C.-ax^2-bx+c=0

5. If the quadratic equation x^2-(4/5)x+(4/k)=0 has real roots and k is positive, then
A.k>25
B.k≧25
C. k<-25

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回答 (1)

用戶9112

2009-10-13 6:29 am

✔ 最佳答案

1. If n<0, which of the following about the roots of the quadratic equation (x+m)^2=-n is correct?
(x + m)^2 = -n
x + m = +-√(-n)
x = -m +-√(-n) (B & D are the same???)
2.If x^2 + 12x + m^2 can be written as a perfect square, then m=
x^2 + 12x + (12/2)^2 + m^2 - (12/2)^2
= (x + 6)^2 + m^2 - 36 is a perfect square
m^2 - 36 = 0
(m - 6)(m + 6) = 0
m = +-6 (B)
3.Which of the following equations has/have one double real root?
I. 5x^2 = 0 => Double roots x = 0
II. x^2 - 5^2 = 0 => Roots = +-5
III.(x-5)^2 = 0 => Double roots x = 5
(C) I and III only
4. If a+b-c=0, then which of the folowing equations has 1 as a root?
Sub 1 into the equation
A. ax^2 + bx + c = 0 => a + b + c = 0 (True)
B. ax^2 - bx - c = 0 => a - b - c = 0 (False)
C.-ax^2 - bx + c = 0 => -a - b + c = 0 (False)
5. If the quadratic equation x^2-(4/5)x+(4/k)=0 has real roots and k is positive, then
D = (4/5)^2 - 4(1)(4/k) > 0
16/25 - 16/k > 0
16/25 > 16/k
k > 25 (A)

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