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so in this video i want to introduce you to the change of sign method a way of locating roots when our algebraic methods have come to nothing okay so lets say that we have our x-axis and weve got a curve that is intersecting the x-axis and this is the root that i am interested in okay this is the point im interested in that x value there okay now this curve lets give it a name lets call it y equals f of x okay and lets say we have this point which well call a and this point well call b okay lets now write it up this way okay then this point that is on the curve is the coordinates a f of a and this point that is on the curve will be b f b okay so what id be saying then is that um if i had substituted in the point a into my curve and id got a positive value then i know that the curve is above the x-axis at that point so if f of a is positive then my curve is above the x-axis there and if i substituted b into my function and i got a value that was negative that would mean that