If $[x]^2 - 5[x] + 6 = 0$, where $[\,.\,]$ denote the greatest integer function, then (A) $x \in [3, 4]$ (B) $x \in (2, 3]$ (C) $x \in [2, 3]$ (D) $x \in [2, 4)$

If [x]² - 5[x] + 6 = 0, where [.] denote the great – Class 11 Mathematics

NCERT Exemplar · Q25

[x]^2 - 5[x] + 6 = 0

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$[x]$ is an integer; solving $[x]^2-5[x]+6=0$ gives $[x]=2$ or $[x]=3$ , so $x\in[2,3)\cup[3,4)=[2,4)$ — option (D).

The greatest integer function $[x]$ returns the largest integer not exceeding $x$ , so $[x]$ is always an integer. Let $[x]=n$ with $n\in\mathbb{Z}$ .

Step 1 — Solve the quadratic in $n$ .

$n^2-5n+6=0\ \Rightarrow\ (n-2)(n-3)=0\ \Rightarrow\ n=2\ \text{or}\ n=3$ …

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Q.If $[x]^2 - 5[x] + 6 = 0$ , where $[\,.\,]$ denote the greatest integer function, then
(A) $x \in [3, 4]$
(B) $x \in (2, 3]$
(C) $x \in [2, 3]$
(D) $x \in [2, 4)$

Concept understanding — The Greatest Integer Function's Defining Property

Q.If [x]2−5[x]+6=0[x]^2 - 5[x] + 6 = 0[x]2−5[x]+6=0, where [ . ][\,.\,][.] denote the greatest integer function, then (A) x∈[3,4]x \in [3, 4]x∈[3,4] (B) x∈(2,3]x \in (2, 3]x∈(2,3] (C) x∈[2,3]x \in [2, 3]x∈[2,3] (D) x∈[2,4)x \in [2, 4)x∈[2,4)

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Q.If $[x]^2 - 5[x] + 6 = 0$ , where $[\,.\,]$ denote the greatest integer function, then
(A) $x \in [3, 4]$
(B) $x \in (2, 3]$
(C) $x \in [2, 3]$
(D) $x \in [2, 4)$

Unlock everything free for 14 days