Question

This section contains 1 paragraph. Based on paragraph, there are 3 questions. Each question has 4 choices (1), (2), (3), (4) out of which only one is correct
Q. if `F(x)` is continuous at `x=+-1`, then `f(x)=g(x)` has
A. imaginary roots
B. both the roots positive
C. roots of opposite sign
D. both the roots negative.

Answer 1

Correct Answer - C
`F(x)={{:(f(x),-1ltxlt1),(g(x),xge1orxlt-1),((f(-1)+g(-1))/(2),x=-1),((f(1)+g(1))/(2),x=1):}`
for continuity at `x=1`
`f(1)=g(1)=(f(1)+g(1))/(2)`
`implies1+a+3=1+bimpliesb=a+3`
Similarly we can check for other questions.