<PRE><B>Question 966543</B>
{{{g(x)=-2x^3-3x+10}}} has a zero between {{{-1}}} and {{{0}}}; 

find the value of {{{g(-1)}}} and {{{g(0)}}}, and see where it (if at all) changes sign, that will be the answer

{{{g(-1)=-2(-1)^3-3(-1)+10}}}
{{{g(-1)=-2(-1)+3+10}}}
{{{g(-1)=2+3+10}}}
{{{g(-1)=15}}}=&gt;{{{g(-1)&gt;0}}}

find the value of {{{g(0)}}}
{{{g(0)=-2(0)^3-3(0)+10}}}
{{{g(0)=0+0+10}}}
{{{g(0)=10}}}=&gt;{{{g(0)&gt;0

as you can see there is {{{no}}} changes in sign, so the answer is {{{g(x)=-2x^3-3x+10}}} does {{{not}}} have a zero between {{{-1}}} and {{{0}}}

or, since {{{g(-1) &gt;0}}} and {{{g(0) &gt; 0}}} and {{{g}}} is a polynomial, the Intermediate Value Theorem tells us that {{{g(x) = 0}}} for some value of {{{x}}} that is {{{not}}} between {{{-1}}} and {{{0}}}

 let&#39;s see it on a graph:

{{{ graph( 600, 600, -25, 25, -25,25, -2x^3-3x+10) }}}

</PRE>