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Question

The number of non-zero solution(s) of the equation x25x6 sgn(x)=0 is (where sgn represents the signum function)

A
2
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B
3
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C
1
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D
0
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Solution

The correct option is C 1
x25x6 sgn(x)=0
We know that,
sgn(x)=1,x<00,x=01,x>0

Case 1: x<0
x25x+6=0
(x2)(x3)=0
x=2,3
But x<0
So, there is no solution.

Case 2: x=0
x25x=0
x(x5)=0
x=0 [x=5 rejected]

Case 3: x>0
x25x6=0
(x+1)(x6)=0
x=6 [x=1 rejected]

Hence, the solutions of the given equation is 0,6
The only non-zero solution is 6.

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