If [x]^2-5[x]+6=0,where [.] denotes the great | vedclass

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Question

(C) Given equation: $[x]^2-5[x]+6=0$ Let $[x] = a$. Then the equation becomes $a^2 - 5a + 6 = 0$. Factoring the quadratic equation: $(a-2)(a-3) = 0$.

Vedclass · Accepted Answer

$x \in[2,4)$

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(C) Given equation: $[x]^2-5[x]+6=0$ Let $[x] = a$. Then the equation becomes $a^2 - 5a + 6 = 0$. Factoring the quadratic equation: $(a-2)(a-3) = 0$. This gives $a = 2$ or $a = 3$. Substituting back $[x] = a$,we get $[x] = 2$ or $[x] = 3$. By the definition of the greatest integer function: If $[x] = 2$,then $x \in [2, 3)$. If $[x] = 3$,then $x \in [3, 4)$. Combining these intervals,we get $x \in [2, 3) \cup [3, 4) = [2, 4)$. Thus,the correct option is $C$.

If $[x]^2-5[x]+6=0$,where $[.]$ denotes the greatest integer function,then

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