topic:relations between the discriminant and the nature of roots.
Question 1:
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.
The ans is :1.2.3 我要個方法點計，要有式 step by step
Question 2:
It is given that the quadratic equation (m- 2)x^2 + mx +2=0 has two
equal real roots.
PartA:find the value of m. Ans is :4
PartB:find the root of the equation. Ans is : -1 repeated
我要個方法點計，要有式 step by step plz.....
F.4 maths 一問,
2009-10-04 10:30 pm
回答 (2)
2009-10-04 10:34 pm
✔ 最佳答案
1. 2x2 - 4x + (c - 1) = 0 has real rootsDiscriminant >= 0
(-4)2 - 4(2)(c - 1) >= 0
c - 1 <= 2
c <= 3
As c is a positive integer, so c = 1, 2 or 3.
2.a. (m - 2)x2 + mx + 2 = 0 has two equal real roots
Discriminant = 0
m2 - 4(m - 2)(2) = 0
m2 - 8m + 16 = 0
(m - 4)2 = 0
m = 4
b. Put m = 4, the equation becomes:
(4 - 2)x2 + 4x + 2 = 0
x2 + 2x + 1 = 0
(x + 1)2 = 0
x = -1 (repeated)
參考: Physics king
2009-10-04 11:39 pm
Question 1: D=b^2-4ac>=0
16-8(c-1)>=0
3>=c
Since c is integer, the possible values of c are 1,2,3
Question 2:
Part A: D=0
m^2-8(m-2)=0
m=4
Part B: Sub. m=4 into the equation
2x^2+4x+2=0
x^2+2x+1=0
x=-1
16-8(c-1)>=0
3>=c
Since c is integer, the possible values of c are 1,2,3
Question 2:
Part A: D=0
m^2-8(m-2)=0
m=4
Part B: Sub. m=4 into the equation
2x^2+4x+2=0
x^2+2x+1=0
x=-1
收錄日期: 2021-04-19 15:27:11
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091004000051KK02778