Let function f(x)=x4+ax3+bx2+cx+d such that f(- 1)=100,f(- 2)=200,f(- 3)=300 then the value (f (10) + f (- 14)/16) equals

Question

Let function f(x)=x4+ax3+bx2+cx+d such that f(- 1)=100,f(- 2)=200,f(- 3)=300 then the value (f (10) + f (- 14)/16) equals (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f(x)=(x + 1)(x + 2)(x + 3)(x + t)-100x for some t P=((11 × 12 × 13 (10 + t) - 1000) + (- 13 × - 12 × - 11 × (t - 14) + 1400)/16) =(11 × 12 × 13 × 24 + 400/16)=2599

Q. Let function $f (x) = x^{4} + a x^{3} + b x^{2} + c x + d$ such that $f (- 1) = 100, f (- 2) = 200, f (- 3) = 300$ then the value $\frac{f ( 10 ) + f ( - 14 )}{16}$ equals

$f (x) = (x + 1) (x + 2) (x + 3) (x + t) - 100 x$ for some $t$
$P = \frac{( 11 \times 12 \times 13 ( 10 + t ) - 1000 ) + ( - 13 \times- 12 \times- 11 \times ( t - 14 ) + 1400 )}{16}$
$= \frac{11 \times 12 \times 13 \times 24 + 400}{16} = 2599$

Q. Let function f(x)=x4+ax3+bx2+cx+d such that f(−1)=100,f(−2)=200,f(−3)=300 then the value 16f(10)+f(−14)​ equals

f(x)=(x+1)(x+2)(x+3)(x+t)−100x for some t P=16(11×12×13(10+t)−1000)+(−13×−12×−11×(t−14)+1400)​ =1611×12×13×24+400​=2599

Q. Let function $f (x) = x^{4} + a x^{3} + b x^{2} + c x + d$ such that $f (- 1) = 100, f (- 2) = 200, f (- 3) = 300$ then the value $\frac{f ( 10 ) + f ( - 14 )}{16}$ equals

$f (x) = (x + 1) (x + 2) (x + 3) (x + t) - 100 x$ for some $t$
$P = \frac{( 11 \times 12 \times 13 ( 10 + t ) - 1000 ) + ( - 13 \times- 12 \times- 11 \times ( t - 14 ) + 1400 )}{16}$
$= \frac{11 \times 12 \times 13 \times 24 + 400}{16} = 2599$