Consider the equation
ax^2 + 4bx - a + 4b = 0
where a, b are integers and a≠0
(a) Prove that the equation has rational roots.
(b) State the condition for the roots to be unequal and write down the two rational roots.
a.maths 問題
2008-02-22 4:56 am
回答 (1)
2008-02-22 6:13 am
✔ 最佳答案
(a)discriminent
=(4b)^2-4a(4b-a)
=16b^2-16ab+4a^2
=(2a-4b)^2
>=0
So the equation has rational roots
(b)
If the roots are unequal
Then discriminent ≠0
Or we can say that b ≠2a
Using the formula
x=[-4b+(2a-4b)]/2a or x=[-4b-(2a-4b)]/2a
x=(2a-8b)/2a or x=-2a/2a
x=a-4b/a or -1
收錄日期: 2021-04-25 16:58:50
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