Question

If f(x) is the polynomial of degree 4 with leading co efficient one satisfying f(1) = 1 , f(2) =2 , f(3) =3 then $\left[\frac{f(-1)+f\left(5\right)}{f\left(0\right)+f\left(4\right)}\right]$

• A. $0$
• B. $2$
• C. $1$
• D. $-1$

Answer 1

The correct option is C $1$

$f\left(x\right)=x$ for $x\in 1,2,3$

$f\left(x\right)-x=0$ for $x\in 1,2,3$

$\therefore f\left(x\right)-x=(x-1)(x-2)(x-3)f\left(x\right)=(x-1)(x-2)(x-3)+xf(-1)=-25f\left(5\right)=29f\left(0\right)=-6f\left(4\right)=10\frac{f(-1)+f\left(5\right)}{f\left(0\right)+f\left(4\right)}=\frac{-25+29}{-6+10}=\frac{4}{4}=1$