 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that, find the 0's of the equation 2 x cube minus 3 x square minus 12 x plus 20 is equal to 0 graphically using graphene calculator. Let us start with the solution of the given question. Here we have to find the 0's or roots of the polynomial equation 2 x cube minus 3 x square minus 12 x plus 20 is equal to 0 graphically using a grapene calculator. First we shall graph this on the calculator. This is the TI 83 plus calculator and we will graph this equation on it. First we begin with home screen and we press y is equal to key. This takes us to the equation entering screen where we will write our equation. Let us enter the equation 2 x cube minus 3 x square minus 12 x plus 20 is equal to 0 into y1. Now we will write this equation using x t theta and key. After writing the equation we will get this screen. To view its graph we press graph key on the screen the graph of the polynomial function y is equal to 2 x cube minus 3 x square minus 12 x plus 20 will appear on the coordinate axis. Now we want to find roots of this equation graphically. Now we know that roots or 0's of function f of x are those points on x axis where f of x is equal to 0. That is on the graph the points of intersection of the curve with x axis will give us real 0's of the given function. Also we should note that only real 0's can be found using graph. Now if we looked at the graph we see that it intersects x axis at one point and at the other point the curve touches the x axis. We also know that if the graph does not cross the x axis and it just touches it then at that point we have a double root. So at this point of the curve we will have double roots. So let us first find this root of the function for this we press second key followed by trace key. We get this display we want to find 0's so we press number 2 key and we get this display of graph. Now it is asking for left bound so we first move the cursor to the left side of the point and then press enter key. The anchor will appear and now it is asking for right bound so we move up from this point and press enter key. Now both anchors appear and it asks for guess so we press enter so on the screen 0 or root is displayed and we get x is equal to 2.0000008 and C y is equal to 0 so we say that 1 0 is x is equal to 2 but curve only touches at this point and does not intersect the x axis so we have double root here. Thus 2 0's of this polynomial equation are x is equal to 2 and 2. Similarly we can find the other 0. Again we press second key followed by trace key and then number 2 key. We will get the following display then we bring cursor down and we press enter key. We get the following display. Now it asks for right bound so we move up and press enter key. Now we get guess on screen and again we press enter key. So now we have real 0 that is at x is equal to minus 2.5 y is equal to 0 so we obtain the real 0 that is x is equal to minus 2.5 thus there are three real 0's for the given equation 2x cube minus 3x square minus 12x plus 20 is equal to 0 and these are x is equal to 2 and minus 2.5. This is the required answer. This completes our session. Hope you enjoyed this session.