A nonzero polynomial with real coefficient has the property that `f(x)=f^(prime)(x)dotf^(prime)(x)dot` If `a` is the leading coefficient of `f(x),` then the value of `1//2a)` is____

Options

A. `1//3`
B. 6
C. 12
D. `1//18`

Answer

D

Explanation

Let degree of f(x) is n,
Degree of `f'(x)` is `n-1`
Degree of `f''(x)` is `(n-1)`
Hence `n=(n-1)+(n-2)=2n-3`
`therefore" "n=3`
`therefore" "f(x)=ax^(3)+bx^(2)+cx+d," "(ane0)`
`" "f'(x)=3ax^(2)+2bx+c`
`" "f''(x)=6ax+2b`
`rArr" "ax^(3)+bx^(2)+cx+d=(3ax^(2)+2bx+c)(6ax+2b)`
`rArr" "18a^(2)=a`
`rArr" "a=1//18`