The number of solutions of `sqrt(3x^(2)+x+5)=x-3` is (A) `0` (B) `1` (C) `2` (D) `4`

Options

A. `0`
B. `1`
C. `2`
D. `4`

Answer

A

Explanation

`(a)` We have `sqrt(3x^(2)+x+5)=x-3`
We must have `3x^(2)+x+5 ge 0` and `x-3 ge 0` or `x ge 3`
`sqrt(3x^(2)+x+3)=x-3` ……….`(i)`
Squaring both sides of `(i)`, we get
`3x^(2)+x+5=x^(2)-6x+9`
`implies 2x^(2)+7x-4=0`
`implies (2x-1)(x+4)=0`
`implies x=1//2,-4`
These values does not satisfy the inequality `x ge 3`.
Thus, `(i)` has no solution.