The number of solutions of the equations of the equation $x^{2} + [x] - 4 x + 3 = 0$ is Where [ ] denotes G.I.F.

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Solution

The correct option is A
0

Given equation can be written as $(x^{2} - 3 x + 3) - f = 0 w h e r e f = x - [x] a n d 0 \leq f$ < 1

$∴ 0 \leq - 3 x + 3$ < 1

solving $x^{2} - 3 x + 3 = 0$ ; roots are Imaginary

$∴ x^{2} - 3 x + 3 \geq 0 \forall x ϵ R$

$s o l v i n g x^{2} - 3 x + 3$ < 1 $\Rightarrow$ < x < 2

if 1 < x < 2; [x]=1 putting [x] = 1 in the given equation and solving we get x = 2. But 1 < x < 2 $∴$ the given equation has no solution.

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