Question

If f(x), g(x), h(x) are polynomials of degree 4 and $\left|\begin{array}{ccc}f\left(x\right)& g\left(x\right)& h\left(x\right)\\ a& b& c\\ p& q& r\end{array}\right|=m{x}^4+n{x}^3+r{x}^2+5x+t$ be an identity in x, then the value of $\left|\begin{array}{ccc}{f}^{\prime \prime \prime }\left(0\right)-f^{\prime \prime }\left(0\right)& g^{\prime \prime \prime }\left(0\right)-g^{\prime \prime }\left(0\right)& h^{\prime \prime \prime }\left(0\right)-h^{\prime \prime }\left(0\right)\\ a& b& c\\ p& q& r\end{array}\right|$ is

• A. (3n-r)
• B. 2(3n-r)
• C. 3(3n-r)
• D. 3n+r

Answer 1

The correct option is B 2(3n-r)

LHS = (24mx + 6n) - (12m$x^2$ + 6nx +2r)
x = 0 $\Rightarrow$ 6n - 2r
$\Rightarrow$ 2(3n-r).