The number of solutions of $$\left| {\left[ x \right] - 2x} \right| = 4,$$ where $$[x]$$ is the greatest integer $$ \leqslant x,$$ is
A.
2
B.
4
C.
1
D.
infinite
Answer :
4
Solution :
$$\eqalign{
& {\text{Given, }}\left| {\left[ x \right] - 2x} \right| = 4 \cr
& \Rightarrow \left[ x \right] - 2x = \pm 4 \cr
& \Rightarrow - \left[ {\left\{ x \right\} + x} \right] = \pm 4 \cr
& {\text{The possible values are }} - 4,\,4,\,3.5,\, - 4.5 \cr
& {\text{So, total 4 values exist}}{\text{.}} \cr} $$
Releted MCQ Question on Algebra >> Quadratic Equation
Releted Question 1
If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are