The correct option is C 1
x2−5x−6 sgn(x)=0
We know that,
sgn(x)=⎧⎨⎩−1,x<00,x=01,x>0
Case 1: x<0
x2−5x+6=0
⇒(x−2)(x−3)=0
⇒x=2,3
But x<0
So, there is no solution.
Case 2: x=0
x2−5x=0
⇒x(x−5)=0
⇒x=0 [x=5 rejected]
Case 3: x>0
x2−5x−6=0
⇒(x+1)(x−6)=0
⇒x=6 [x=−1 rejected]
Hence, the solutions of the given equation is 0,6
The only non-zero solution is 6.