Find real solutions for $x$, in$ \,\,\,f(x)=2x^{98}+5x^{97}+5x^{96}+...5x+3=0$, It is also given that $x+1$ is a factor
Since $x+1$ is a factor, we can write $f(x) =(x+1)(2x^{97}+3x^{96}+2x^{95}...+3)$
can someone give a hint what to do next? Thanks.
$f(x)=5x(x^{97}+x^{96}+...+x+1)+3-3x^{98}=5x \frac{1-x^{98}}{1-x}+3(1-x^{98})$ for $x \ne 1$.
Can you proceed ?