For certain real numbers a, b and c, the polynomial  $g\left(x\right)=x^3+a{x}^2+x+10$  has three distinct roots, and each root of g(x) is also a root of the polynomial  $f\left(x\right)=x^4+x^3+b{x}^2+100x+c$.The value of f(1) is_____

g (x) = (x – a) (x – b) (x – c)
f (x) = g (x) h (x)
$$\begin{gathered} x^4+x^3+b{x}^2+100x+c=(x^3+a{x}^2+x+10)(x+r) \\ {x}^4+x^3+b{x}^2+100x+c-(x^3+a{x}^2+x+10)(x+r)=0 \end{gathered}$$
$x^3:1-(a+r)=0$ and x : 100 – (10 + r) = 0
$\Rightarrow$  r = 90, a = – 89 
$g\left(x\right)=x^3-89x^2+x+10$
g (1) = 1 + a + 1 + 10 = 1 – 89 + 1 + 10 = –77
h (1) = 1 + r = 1 + 90 = 91
f (1) = g (1) h (1) = –77.91 = $\boxed{-7007}$