Answer
$f(a)=f(1.4)=-0.1754\lt 0$ and
$f(b) =f(1.5)=1.4063\gt 0$
Since function values have opposite signs at the endpoints of the interval, by the Intermediate Value Theorem,
there is at least one real zero of $f$ between $1.4$ and $1.5.$
Work Step by Step
Intermediate Value Theorem
Let $f$ be a polynomial function.
If $a\lt b$ and if $f(a)$ and $f(b)$ are of opposite sign, there is at least one real zero of $f$ between $a$ and $b.$
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Using a calculator,
$f(a)=f(1.4)=-0.1754\lt 0$ and
$f(b) =f(1.5)=1.4063\gt 0$
Since function values have opposite signs at the endpoints of the interval, by the Intermediate Value Theorem,
there is at least one real zero of $f$ between $1.4$ and $1.5.$
