# find set of values, district roots

• January 12th 2012, 10:35 AM
andyboy179
find set of values, district roots
hi,

i nned to know how to answer this question:

Find a set of values of x for the equation have two district roots, x^2-6x+k=0

im not too sure how i would complete this question, so could someone provide some help please?

thanks!
• January 12th 2012, 10:38 AM
e^(i*pi)
Re: find set of values, district roots
Quote:

Originally Posted by andyboy179
hi,

i nned to know how to answer this question:

Find a set of values of x for the equation have two district roots, x^2-6x+k=0

im not too sure how i would complete this question, so could someone provide some help please?

thanks!

If it has two distinct roots then the discriminant must be greater than 0: $b^2 - 4ac > 0$

Where a=1, b=-6, c=k
• January 12th 2012, 11:14 AM
andyboy179
Re: find set of values, district roots
-6^2-4x1x4>0
-36+-16>0
-52>0?
• January 12th 2012, 11:33 AM
skeeter
Re: find set of values, district roots
Quote:

Originally Posted by andyboy179
-6^2-4x1x4>0
-36+-16>0
-52>0?

a = 1 , b = -6 , c = k

order of operations? try again ...

$(-6)^2 - 4(1)(k) > 0$
• January 12th 2012, 11:48 AM
andyboy179
Re: find set of values, district roots
oh poo!

-6^2-4x1xk>0
-36+-4k>0
>36+4k
36/4= 9
K=9?
• January 12th 2012, 11:53 AM
skeeter
Re: find set of values, district roots
Quote:

Originally Posted by andyboy179
oh poo!

-6^2-4x1xk>0
-36+-4k>0
>36+4k 36/4= 9
K=9?

no ...

1. apparently, you do not understand the difference between $(-6)^2$ and $-6^2$.

2. $+4k$?

3. you are solving an inequality ... where did the equal sign come from?
• January 12th 2012, 12:04 PM
andyboy179
Re: find set of values, district roots
-6^2-4x1xk>0
36+-4k>0
36>4k
36/4= 9
k>9?
• January 12th 2012, 12:42 PM
e^(i*pi)
Re: find set of values, district roots
Quote:

Originally Posted by andyboy179
-6^2-4x1xk>0
36+-4k>0
36>4k
36/4= 9
k>9?

You changed the direction of the inequality in the last line but there is no need to since you were dividing by +4.

$k < 9$
• January 12th 2012, 01:02 PM
andyboy179
Re: find set of values, district roots
so what would be the set of values for x?
• January 12th 2012, 01:13 PM
e^(i*pi)
Re: find set of values, district roots
Quote:

Originally Posted by andyboy179
so what would be the set of values for x?

That's a good question, are you sure the question doesn't ask for the values of k instead of x?

When we work out the nature of the roots (whether they're real/distinct) it's the coefficients of x that matter rather than values of x itself
• January 12th 2012, 01:42 PM
andyboy179
Re: find set of values, district roots
it is definetly x! umm im not too sure how to do the next part then.