Question 970034
{{{f(x)=x^5-x^4+5x^3-4x^2-20x+18}}}:  interval:[{{{1.5}}},{{{1.9}}}] 

if {{{x=1.5}}},

{{{f(1.5)=(1.5)^5-(1.5)^4+5(1.5)^3-4(1.5)^2-20(1.5)+18}}}
{{{f(1.5)=-1.59375}}}

if {{{x=1.9}}},

{{{f(1.9)=(1.9)^5-(1.9)^4+5(1.9)^3-4(1.9)^2-20(1.9)+18}}}
{{{f(1.9)=11.58389}}}

Now we know:

    at {{{x=1.5}}}, the curve is {{{below}}} zero
    at {{{x=1.9}}}, the curve is {{{above}}} zero

And, being a polynomial, the curve will be {{{continuous}}}.
So, somewhere in between, the curve {{{must}}} cross through {{{y=0}}}


{{{drawing( 600, 600, -5, 5, -15, 15, 
circle(1.5,0,.08),circle(1.9,0,.08),circle(1.59204,0,.08),
locate(1.59204,0.8,p(1.59204,0)),
 graph( 600, 600, -5, 5, -10, 10, x^5-x^4+5x^3-4x^2-20x+18)) }}}

zero is at {{{x=1.59204}}} and {{{1.5<1.59204<1.9}}}