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Greatest Integer Function

If x∈[0, 10],...

Question

If $x \in [0, 10]$ , then the number of integral value(s) of $x$ satisfying the equation $x^{2} + 4 x + [x] + 6 = 0$ (where [.] denotes the greatest integer function) is

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Solution

From the given interval of $x$
$[x] \geq 0; x^{2} \geq 0; 4 x \geq 0 \Rightarrow x^{2} + 4 x + [x] \geq 0 \Rightarrow x^{2} + 4 x + [x] + 6 \geq 6$
Hence no solution exists

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