A) (4, 5)
B) (3, 4)
C) (5, 6)
D) None of these
Correct Answer: D
Solution :
\[{{x}^{2}}-mx+4=0\] |
\[a,\beta \in [1,5]\] |
[a] D < 0 \[\Rightarrow \]\[{{m}^{2}}-16>0\] |
\[\Rightarrow \]\[m\in \,(-\infty ,-\,4)\cup \,(4,\infty )\] |
[b] \[f(1)\ge 0\] \[\Rightarrow \]\[5-m\ge 0\] |
\[\Rightarrow \] \[m\in \,(-\,\infty ,5)\] |
[c] \[f\,(5)\ge 0\]\[\Rightarrow \] \[29-5m\ge 0\] |
\[\Rightarrow \] \[m\in \left( -\,\infty ,\left. \frac{29}{5} \right] \right.\] |
[d] \[1<\frac{-\,b}{2a}<5\] \[\Rightarrow \] \[1<\frac{m}{2}<5\] |
\[\Rightarrow \] \[m\in \,(2,10)\] |
\[\Rightarrow \] \[m\in \,(4,5)\] |
No option correct : Bonus |
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