First slide

Theory of expressions

Question

If $[x]$ denotes the greatest integer $\leq x,$ and $a, b$ are two odd integers, then number of solutions of ${[x]}^{2} + a [x] + b = 0$ is

Moderate

A

1
B

0
C

2
D

infinite

Solution

If $[x]$ is odd, then
${[x]}^{2} + a [x] + b$ is odd and if $[x]$ ] is even, then ${[x]}^{2} + a [x] + b$ is also odd
Thus, ${[x]}^{2} + a [x] + b$ can never take value $0$ .

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