Question 140328
{{{p(x)=2x^3-4x^2+5x-6}}} Start with the given equation



{{{p(-1)=2(-1)^3-4(-1)^2+5(-1)-6}}} Plug in {{{x=-1}}}



{{{p(-1)=-17}}} Multiply and combine like terms



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{{{p(x)=2x^3-4x^2+5x-6}}} Go back to the given equation



{{{p(2)=2(2)^3-4(2)^2+5(2)-6}}} Plug in {{{x=2}}}



{{{p(2)=4}}} Multiply and combine like terms




Since {{{p(-1)=-17}}} (which is negative) and {{{p(2)=4}}} (which is positive), this means that the graph has crossed the x-axis. So there is a zero in between -1 and 2