Hi friends,

I have something that tickles me....please help:

if I look at \(x^2-4x-5=0\)

and I wanted to check the nature of the roots by solving the equation, it would be like this:

\((x+1)(x-5)=0\)

\(x=-1\) or \(x=5\)

So all I can really say is that the roots are un-equal

However doing it this way:

\(\Delta =b^2-4ac\)

\(=(-4)^2-4(1)(-5)\)

\(=16+20\)

\(=36\)

which means the roots will be real, un-equal and rational...However, the roots do only seem to satisfy the "un-equal" nature?

juriemagic Jun 2, 2021

#1**+1 **

Notice though that b^2 -4ac is under a radical......so sqrt (36) = 6

So.....the roots will be real, rational AND unequal

CPhill Jun 2, 2021

#2**+1 **

Hi CPhill,

thank you for the response, I guess I'm getting thrown off track with the fact that I thought the roots had to be squares themselves. my error, thank you kindly..

juriemagic
Jun 2, 2021