Paragraph: Let f(x)= (a x^2+b x+c ) sgn (2 x-1) be a continuous function x (0,6) where a, b, c R . [Note: sgn (.) represents signum function.] Question: If c=0 , then (a+b) equals:

Step-by-step solution

aligned & f(x)= (a x^2+b x+c ) sgn (2 x-1) & f(x)=- (a x^2+b x+c ), 0 < x < 6 & f(x)=0, x= 6 & f(x)= (a x^2+b x+c ), 6 < x < 5 6 & f(x)=0, x= 5 6 aligned f(x)=- (a x^2+b x+c ), 5 6 < x < 6 If y=f(x) is continuous, then a x^2+b x+c=a (x- 6 ) (x- 5 6 ) If c=0 a=b=0