Question
Question: The equation x³- 6x² + 9x + 1 = 0 have exactly one root in (1,3) then find the number of integral va...
The equation x³- 6x² + 9x + 1 = 0 have exactly one root in (1,3) then find the number of integral values of [2+1] (where [.] denotes the greatest integer function)
A
1
B
2
C
3
D
4
Answer
1
Explanation
Solution
The expression to be evaluated is [2+1].
First, calculate the value inside the greatest integer function: 2 + 1 = 3.
Then, apply the greatest integer function: [3] = 3.
The question asks for the number of integral values of 3. Since 3 is an integer, there is exactly one integral value, which is 3 itself.
The condition about the cubic equation having a root in (1,3) is irrelevant to the evaluation of the constant expression [2+1].
Therefore, the number of integral values of [2+1] is 1.