If - x 2- x - a -0 has a solution - represents the greatest integer function- where a - N - a - 20- then the total number of distinct values of a isA- 2B- 3C- 4D- 6

The correct option is C 4[x^2]+x a=0 ⇒ [x^2] a= x L.H.S. is an integer. So, x has to be an integer. ∴ a=x^2+x ⇒ a = x (x+1) As a≤ 20, ∴ a = 2,6,12, 20 at x=1, ...

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Standard XII

Mathematics

Greatest Integer Function

If [ x 2]+ x ...

Question

If $[x^{2}] + x - a = 0$ has a solution $([.]$ represents the greatest integer function $)$ , where $a \in N, a \leq 20$ , then the total number of distinct values of $a$ is

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Solution

The correct option is C $4$
$[x^{2}] + x - a = 0$
$\Rightarrow [x^{2}] - a = - x$
L.H.S. is an integer.
So, $x$ has to be an integer.
$∴ a = x^{2} + x$
$\Rightarrow a = x (x + 1)$
As $a \leq 20$ ,
$∴ a = 2, 6, 12, 20 at x = 1, 2, 3, 4$ respectively.

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If [x2]+x−a=0 has a solution ( [.] represents the greatest integer function), where a∈N, a≤20, then the total number of distinct values of a is

The correct option is C 4[x2]+x−a=0 ⇒[x2]−a=−x L.H.S. is an integer. So, x has to be an integer. ∴a=x2+x ⇒a=x(x+1) As a≤20, ∴a=2,6,12,20 at x=1,2,3,4 respectively.

If $[x^{2}] + x - a = 0$ has a solution $([.]$ represents the greatest integer function $)$ , where $a \in N, a \leq 20$ , then the total number of distinct values of $a$ is

The correct option is C $4$
$[x^{2}] + x - a = 0$
$\Rightarrow [x^{2}] - a = - x$
L.H.S. is an integer.
So, $x$ has to be an integer.
$∴ a = x^{2} + x$
$\Rightarrow a = x (x + 1)$
As $a \leq 20$ ,
$∴ a = 2, 6, 12, 20 at x = 1, 2, 3, 4$ respectively.