1)in each of the following,find the value or range of values of the constant d so that the given statment is true.
a)(1-d)x^2 - 2(2-d)x + (1-d)=0 has no real roots.
2)the quadratic equation (k+2)x^2 - (k-1)x + 1=0 has equal roots.
a)when k is negative,slove the given equation.
3)if the equation x((2k-1)x+3)(3k+1)+9=0 has equal roots,find
a)the value of k,
b)the roots of the equation.
maths
2007-09-05 6:55 am
回答 (1)
2007-09-05 7:13 am
✔ 最佳答案
1(a) Discriminant = 4(2-d)^2 - 4(1-d)(1-d) < 0(4-4d+d^2) - (1-2d+d^2) < 0
3 - 2d < 0
d>3/2
2(a) Discriminant = (k-1)^2 - 4(k+2)(1) = 0
k^2 - 2k + 1 - 4k - 8 = 0
k^2 - 6k - 7 = 0
(k-7)(k+1) = 0
k = 7 (rejected, as k<0) or -1
When k = -1, the equation becomes x^2 +2x+1 = 0
(x+1)^2 = 0
x = -1
3 (a) (2k-1)(3k+1)x^2 + 3(3k+1)x + 9 = 0
Discriminant = 9(3k+1)^2 - 4(9)(2k-1)(3k+1) = 0
9(3k+1)(3k+1-8k+4) = 0
9(3k+1)(5-5k) = 0
k = 1 or -1/3
When k = -1/3, the equation becomes x(-5/3 x +3)(0) + 9 = 9, which is not equal to 0.
Therefore k = 1.
(b) When k = 1, the equation becomes 4x^2 + 12x + 9 = (2x+3)^2 = 0
x = -3/2
參考: me
收錄日期: 2021-04-13 18:13:14
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070904000051KK04616