MHT CET · Maths · Functions
If \(f(x)=[x]^{2}-5[x]+6=0\), where \([x]\) denotes greatest integer function
then \(x \in\)
- A \((2,4]\)
- B \([2,4]\)
- C \([2,4)\)
- D \((2,4)\)
Answer & Solution
Correct Answer
(C) \([2,4)\)
Step-by-step Solution
Detailed explanation
We have, \([x]^{2}-5[x]+6=0\)
\(\therefore([x]-3)([x]-2)=0 \Rightarrow[x]=2,3\)
For \([x]=2, x \in[2,3)\) and for \([x]=3, x \in[3,4)\)
\(\therefore \quad x \in[2,4)\)
\(\therefore([x]-3)([x]-2)=0 \Rightarrow[x]=2,3\)
For \([x]=2, x \in[2,3)\) and for \([x]=3, x \in[3,4)\)
\(\therefore \quad x \in[2,4)\)
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