# A quartic function

#### anemone

##### MHB POTW Director
Staff member
Prove that there is no root exists in the interval $(0,2)$ for a quartic function $k^4-10+k-3k^2$.

#### mathbalarka

##### Well-known member
MHB Math Helper
Sturm's theorem gives 0. But I have no intention of calculating here that with whole details as I have done in my notebook, so I simply leave it to someone else

#### anemone

##### MHB POTW Director
Staff member
Prove that there is no root exists in the interval $(0,2)$ for a quartic function $k^4-10+k-3k^2$.
My solution:

If we let $0<k<2$,

#### anemone

##### MHB POTW Director
Staff member
I have a slightly different approach...
Hey agentmulder, thanks for participating!

I say your method is more straightforward and smarter than mine, well done!

Btw, would you mind to hide your solution? Thanks.