Question

A non zero polynomial f(x) with real coefficients satisfy f(x) = $f^{\prime }\left(x\right)f^{\prime \prime }\left(x\right)$ and f(0) = 96. If 'a' is the coefficient of highest degree term of f(x), then

• A. $a=\frac{1}{18}$
• B. $f^1(-6)=6$
• C. $f^{11}\left(3\right)=5$
• D. $f\left(1\right)=10$

Answer 1

Answer: (A), (C)

The correct options are
A $a=\frac{1}{18}$
C $f^{11}\left(3\right)=5$

Let degree of f(x) be n.
$\therefore n=(n-1)+(n-2)\Rightarrow n=3$
Hence f(x) $=a{x}^3+b{x}^2+cx+96[\because f(0)=96]$
Apply f(x) = $f^{\prime }\left(x\right).f^{\prime \prime }\left(x\right)\Rightarrow a=\frac{1}{18},b=2,c=24$