If `f(x)=x^2+x+3/4` and `g(x)=x^2+a x+1` be two real functions, then the range of `a` for which `g(f(x))=0` has no real solution is `(-oo,-2)` b. `(-2,2)` c. `(-2,oo)` d. `(2,oo)`

Options

A. `(-oo,-2)`
B. `(-2,2)`
C. `(-2,oo)`
D. `(2,oo)`

Answer

C

Explanation

`f(x)=x^(2)+x+(3)/(4)=(x+(1)/(2))^(2)+(1)/(2)ge(1)/(2)`
`g(f(x))=f(x)^(2)+af(x)+1`
for g(f(x))=0,
`a=-(f(x)+(1)/(f(x)))le-2`
`therefore` If `a gt -2, g(f(x))=0` has no solutions