a maths questions
2008-05-04 10:56 pm
If the equation ax^2+bx+c=0 has real rots, show that the roots of the equation a^2x^+(2ac-b^2)x+c^2=0 are real.
回答 (1)
2008-05-04 11:57 pm
✔ 最佳答案
∵The equation ax2+bx+c=0 has real rots∴∆≥0
i.e. b2-4ac≥0
The equation a2x2+(2ac-b2)x+c2=0,
∆=(2ac-b2)2-4(a2)(c2)
=4a2c2-4acb2+b4-4a2c2
=b4-4acb2
=b2(b2-4ac)
≥0(∵b2-4ac≥0)
So,the equation a2x2+(2ac-b2)x+c2=0 has real roots.
收錄日期: 2021-04-23 20:32:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080504000051KK01590