F4 maths - Ans.fyi 參考答案

F4 maths

2009-11-02 5:54 am

1. If the graph of y= -2x^2+12x+c and the x-axis intersect at two points, find the range of values of c.

2. Given that the graph of y= ax^2-6x+5 does not intersect the x-axis, find the minimum value of a if it is an integer.

3. Given that the equation 2x^2-4x+(c-1)=0 has real roots, find all the possible values of c if it is a positive integer.

回答 (1)

Prof. Physics

2009-11-02 5:59 am

✔ 最佳答案

1. y = -2x^2 + 12x + c

It intersects the x-axis at two points.

So, -2x^2 + 12x + c = 0 has two distinct real roots

Discriminant > 0

(-12)^2 - 4(-2)c > 0

144 + 8c > 0

16 + c > 0

c > -16

2. y = ax^2 - 6x + 5 does not intersect the x-axis.

That is, ax^2 - 6x + 5 = 0 has no real root

Discriminant < 0

(-6)^2 - 4a(5) < 0

36 - 20a < 0

9 - 5a < 0

5a > 9

a > 9/5

3. 2x^2 - 4x + (c - 1) = 0 has real roots,

Discriminant >= 0

(-4)^2 - 4(2)(c - 1) >= 0

16 - 8(c - 1) >= 0

24 - 8c >= 0

8c <= 24

c <= 3

So, the possible values of c are 1, 2 or 3.

參考: Physics king

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