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

Explanation

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