Answer
There is a root of the equation $x^4 + x − 3=0$ in the
interval$ (1, 2)$
Work Step by Step
Given:
$f(x) = x^4 + x − 3$
The above function is continuous on the interval $[1, 2]$,
$f(1) = (1)^4+(1)-3$
$= 1+1-3$
$=2-3$
$f(1)=-1$,
and,
$f(2) =2^4+2-3$
$=16+2-3$
$=18-3$
$f(2)=15$.
Since $−1 <0 < 15$, there is a number $c$
in $(1, ~2)$ such that $f(c)=0$ by the Intermediate Value Theorem. Thus, there is a root of the equation $x^4 + x − 3=0$ in the
interval$ (1, 2)$
