# Find K so that....

• Jul 17th 2012, 03:47 PM
waleedrabbani
Find K so that....
X^3 -12X^2 + K

find K for
Two Different Zeros
Three Different Zeros ( I believe K=X for this one )
Only one Real Zero

Any help would be greatly appreciated thanks
• Jul 17th 2012, 04:27 PM
Wilmer
Re: Find K so that....
Quote:

Originally Posted by waleedrabbani
X^3 -12X^2 + K

Is that suppose to be X^3 - 12X^2 + K = 0 ?
You're not showing an equation!!

Anyhow, if K=0 then:
x^3 - 12x^2 = 0
x^2(x - 12) = 0
• Jul 17th 2012, 04:31 PM
Reckoner
Re: Find K so that....
Quote:

Originally Posted by waleedrabbani
X^3 -12X^2 + K

find K for
Two Different Zeros
Three Different Zeros ( I believe K=X for this one )
Only one Real Zero

The discriminant of the cubic equation $ax^3 + bx^2 + cx + d = 0$ is given by

$d = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2.$

So the cubic equation $X^3 - 12X^2 + K$ has a discriminant of

$d = 6912K - 27K^2.$

Now determine which values of $K$ make the discriminant positive, negative, or zero.