oops, another tricky one...

[smilyfacebkwrm]

given a polynomial P such that P(a) < 0 and P(b) >0 we can use a method called linear interpolation to estimate the zero between a and b. As the name implies, this method assumes that the graph of P is approximately linear between a and b. Show that this x-intercept is x= -(P(a) * (b-a)) / (P(b) - P(a))

thanks for any help...

 

[Unco]

Assuming you mean x= -(P(a) * (b-a)) / (P(b) - P(a)) + a,

You have two coordinates: (a, P(a)) and (b, P(b)).

You can find the equation of the line joining those points (using (a, P(a)) may be easier for you).

You can figure out the next part.