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- Feb 14, 2012
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Prove that there is no root exists in the interval $(0,2)$ for a quartic function $k^4-10+k-3k^2$.
My solution:Prove that there is no root exists in the interval $(0,2)$ for a quartic function $k^4-10+k-3k^2$.
We have $k(k-2)<0$. | Besides, we also have $k^3(k-2)<0$ |
Adding 1 to the inequality $0<k<2$ we get $1<k+1<3$. Or simply $k+1>0$. Thus, $k(k-2)(k+1)<0$ $k^3-k^2-2k<0$ $k^3<k^2+2k$ $2k^3<2k^2+4k$ (*) | Expanding the inequality we get $k^4-2k^3<0$ $k^4<2k^3$(**) |
Hey agentmulder, thanks for participating!I have a slightly different approach...