F4 Nature of roots
2011-10-13 3:26 am
form a quadratic equation in x whose roots are the sum of the product of the roots of -3x^2+1/4x+1=0 respectively.
回答 (2)
2011-10-13 4:43 am
✔ 最佳答案
-3x^2 + (1/4)x + 1 = 0Sum of roots = 1/12
Product of roots = -1/3
So, the roots of the new equation are 1/12 and -1/3
Sum of the new roots = 1/12 - 1/3 = -1/4
Product of the new roots = (1/12)(-1/3) = -1/36
So, the new equation is
x^2 + (1/4)x - 1/36 = 0 or
36x^2 + 9x - 1 = 0
2011-10-13 3:51 am
-12x^2+x+4
sum of roots=1/12
product of roots=-4/12
New sum of roots=1/12-4/12=-3/12=-1/4
New product of roots=(1/12)*-4/12=-1/36
The new quadratic equation is x^2+x/4-1/36=0
9x^2+x-1=0
sum of roots=1/12
product of roots=-4/12
New sum of roots=1/12-4/12=-3/12=-1/4
New product of roots=(1/12)*-4/12=-1/36
The new quadratic equation is x^2+x/4-1/36=0
9x^2+x-1=0
收錄日期: 2021-04-13 18:17:39
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111012000051KK00603