- #1

davon806

- 148

- 1

I am trying to solve x^2 - 10x + 26 < 0

Here are my steps:

1.Find the roots of x by using quadratic formula:

x = [10 ± √(100-104)]/2

= 5±i

2.Rewrite x^2 - 10x + 26 into [x-(5+i)][x-(5-i)]

3.Now we have:

[x-(5+i)][x-(5-i)]<0

x-(5+i) < 0 and x-(5-i) > 0 or x-(5+i) > 0 and x-(5-i) < 0

x < 5+i and x > 5-i or x>5+i and x<5-i (rejected)

So we get the answer 5-i<x<5+i

Here is the bit that I found weird:

When x = 5,

5-i<5+0i<5+i

∴x^2 - 10x + 26 = 25 - 50 + 26

= 1

1>0?What's wrong with the above steps?

Thx a lot!