The equation $x^2-4 x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has :
- no solution
- exactly two solutions in $(-\infty, \infty)$
- a unique solution in $(-\infty, 1)$
- a unique solution in $(-\infty, \infty)$
The Correct Option is D
Approach Solution - 1
Only one solution in
Approach Solution -2
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
