F.4 Maths - Ans.fyi 參考答案

F.4 Maths

[匿名]

2012-07-15 2:04 am

1. Let c be a constant. If the difference between the two roots of the equation 2x^2+5x+c=0 is 19/2 , (a) find the roots of the equation. (b) find the value of c

2. If k is a constsnt and a root of the equation -3x^2+(7-k)x+k =0 is the reciprocal of the other root, (a) find the value of k. (b) find the two roots of the equation.

3. It is given that the difference between the ten digit and the units digits of a two-digit number is 2. The tens digit is smaller than the units digit. Let x be the tens digit. (a) Express the value of the two digit number in terms of x.
(b) If the two-digit number is equal to three times the product of its tens and units digits , find the number.

回答 (1)

用戶30507

2012-07-15 2:54 am

✔ 最佳答案

1. Let the two roots be α and α+19/2.
(a) sum of roots of the equation 2x^2+5x+c=0 is -5/2
⇒ α+(α+19/2)=-5/2
⇒α=-6
Ans: the roots are -6 and -6+19/2, i.e. -6 and 7/2

(b) product of roots = c/2
⇒-6×7/2=c/2
⇒c=-42

2. Let the two roots be α and 1/α.
(a) product of roots = k/(-3)=α (1/α)
⇒-k/3=1
⇒k=-3

(b) Putting k=-3 into the equation, we have
-3x^2+(7-(-3))x+(-3) =0
-3x^2+10x-3 =0
(3x-1)(x-3)=0
the roots are 1/3 and 3.

3. Given the tens digit is x. Thus the units digit is x+2.
(a) The value of the two-digit number=10x+(x+2)=11x+2

(b) From given, 11x+2=3(x)(x+2).
∴3x²-5x-2=0
(3x+1)(x-2)=0
x=2 or x=-1/3 (rejected)
∴the tens digit is 2 and the units digit is 2+2=4
Ans: the number is 24.

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