consider the function f(X) =`3x^(4)+4x^(3)-12x^(2)`
The range of values of a for which f(x) = a has no real

Options

A. `(4,oo)`
B. `(10,oo)`
C. `(20,oo)`
D. none of these

Answer

4

Explanation

`f(x)=3x^(4)+4x^(3)-12x^(2)`
`therefore f(X)=12(x^(3)+x^(2)-2x)=12x(x-1)(x+2)`
The sign scheme of f(X) is as follows

The graph of the funciton is as follows

Thus we have
f(-2)=-32 and f(1)=-5
Hence range of hte function is `[-32,oo)`
Also f(x)= a has real roots if `alt-32`