MHT CET · Maths · Functions
If \([x]^2-5[x]+6=0\), where [.] denotes the greatest integer function, then
- A \(x \in(2,4]\)
- B \(x \in[2,4]\)
- C \(x \in[2,4)\)
- D \(x \in(2,4)\)
Answer & Solution
Correct Answer
(C) \(x \in[2,4)\)
Step-by-step Solution
Detailed explanation
Given:
\(\begin{aligned}
& {[x]^2-5[x]+6=0} \\
& \text { Let }[x]=\mathrm{a} \\
& \Rightarrow \mathrm{a}^2-5 \mathrm{a}+6=0 \\
& \Rightarrow(\mathrm{a}-2)(\mathrm{a}-3)=0 \\
& \Rightarrow \mathrm{a}=2 \text { or } \mathrm{a}=3 \\
& \Rightarrow[x]=2 \text { or }[x]=3 \\
& \Rightarrow x \in[2,3) \text { or } x \in[3,4) \\
& \Rightarrow x \in[2,4)
\end{aligned}\)
\(\begin{aligned}
& {[x]^2-5[x]+6=0} \\
& \text { Let }[x]=\mathrm{a} \\
& \Rightarrow \mathrm{a}^2-5 \mathrm{a}+6=0 \\
& \Rightarrow(\mathrm{a}-2)(\mathrm{a}-3)=0 \\
& \Rightarrow \mathrm{a}=2 \text { or } \mathrm{a}=3 \\
& \Rightarrow[x]=2 \text { or }[x]=3 \\
& \Rightarrow x \in[2,3) \text { or } x \in[3,4) \\
& \Rightarrow x \in[2,4)
\end{aligned}\)
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