1. (a) Find the range of values of k if the expressive 4x^2+2(k+3)x+9k^2 is positive for all real values of x.
(b) Find the range of values of x if the expressive 4x^2+2(k+3)x+9k^2 is positive for all real values of k.
2. Let f(x) = ax^2-12x+c, where a and c are real constants.
(a) If f(x) has the maximum value 10 when x= -3/2, find the values of a and c.
(b) If the roots of the equation f(x) =0 are A and B, find the quadratic equation whose roots are A^2 and B^2.
A. maths (urgent)
2007-10-29 3:11 am
回答 (2)
2007-10-29 3:32 am
✔ 最佳答案
1(a) Discriminant = [2(k+3)]^2 -4(4)(9k^2) < 04(k^2 + 6k +9) - 4(36k^2) < 0
35k^2 - 6k - 9 > 0
(7k+3)(5k-3) > 0
k< -3/7 or k > 3/5
(b) 4x^2+2(k+3)x+9k^2 = 9k^2 + 2xk + (6x+4x^2)
Discriminant = (2x)^2 - 4(9)(6x+4x^2) < 0
4x^2 - 4(54x+36x^2) < 0
-35x^2 - 54x < 0
35x^2+54x > 0
x(35x+54) > 0
x< -54/35 or x > 0
2. f(x) = ax^2 - 12x + c = a(x^2 - (12/a) x + (6/a)^2) + c - a(6/a)^2
= a(x-6/a)^2 + c - 36/a
If f(x) is maximum at x = -3/2 and its value is 10
6/a = -3/2 and c - 36/a = 10
a = -4 and c - 36/(-4) = 10
c +9 = 10
c = 1
(b) f(x) = -4x^2 - 12x + 1 = 0
4x^2 + 12x - 1 = 0
A+B = -12/4 = -3
AB = -1/4
A^2 + B^2 = (A+B)^2 - 2AB = 9+1/2 = 19/2
A^2B^2 = (-1/4)^2 = 1/16
The required equation is
x^2 - 19/2 x + 1/16 = 0
16x^2 - 152x + 1 = 0
2007-10-29 3:18 am
answer:758+1652=2410
收錄日期: 2021-04-13 18:12:32
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071028000051KK04175