Question

How many roots do. the following equations possess?
$x^4+x^3=10.$

Answer 1

$x^4+x^3=10$ (given)

$f\left(x\right)=x^4-x^3-10=0$

$f\left(1\right)=-10$ , $f\left(2\right)=16-8-10=-2$ , $f\left(3\right)=81-27-10=44$

As $f\left(x\right)$ changes sign from $f\left(2\right)$ to $f\left(3\right)$. So, Root lies b/w $(2,3)$. ONLY 1 ROOT