Question

The value of $a_{99}$ is equal to ?

• A. $2^{98}$
• B. $2^{99}$
• C. ${-2}^{99}$
• D. $None$

Answer 1

The correct option is C ${-2}^{99}$

$a_0+a_{1}x+a_2{x}^2+\cdots +a_{99}{x}^{99}+x^{100}=0$

$hasroots{}^{99}{C}_0,{}^{99}{C}_1,{}^{99}{C}_2\dots {}^{99}{C}_{99}$

$So{x}^{100}+a_{99}{x}^{99}+a_{98}{x}^{98}+\dots +a_2{x}^2+a_{1}x+a_0=0$

$Sumofrootsinanequation=\frac{-a_{99}}{1}So\frac{a^9{C}_0{+}^{99}{C}_1+\dots {-}^{99}{C}_{99}}{1}$

$-2^{99}=a_{99}$