 Hi and welcome to the session. I am Arsha and I am going to help you solve the following problem which says find the zero of the polynomial in each of the following cases. Suppose let us learn what is the zero of the polynomial. Suppose we have any polynomial Px, x is equal to c where c is any number is called the zero of Px, Pfc is equal to zero. So this is our key idea with the help of which we will find the zero of the above given linear equations. Let us now start with the solution and the first one is Px is equal to x plus 5. Now here we are required to find the zero of Px that is zero of Px implies the value of x such that when x is replaced by the value P that the value of this polynomial comes out to be zero. So for that we will substitute Px is equal to zero or x plus 5 is equal to zero which further implies x is equal to minus 5 and so x is equal to minus 5 is a zero of Px. Since I am replacing x by minus 5 we get the value of the polynomial Px is zero so x is equal to minus 5 is the zero of Px. So this completes the first part. Now proceeding on to the second part where Px is equal to x minus 5. Again here we need to find the zero of Px that is the value of x such that on substituting the value of x the value of the polynomial comes out to be zero. So to get that value of x we will solve Px is equal to zero x minus 5 is equal to zero which further implies that x is equal to 5. That is why I am replacing x by 5 in this equation we get the value of the polynomial as zero hence x is equal to 5 as a zero of the given polynomial Px which is equal to x minus 5. Now proceeding on to the third part which is Px is equal to 2x plus 5. Again to find the value of x such that on replacing it by x we get the value of the polynomial as zero we will have to solve x is equal to zero or this implies that 2x plus 5 is equal to zero or 2x is equal to minus 5 or x is equal to dividing both sides by 2 which further gives 2 cancels out with 2 or we have x is equal to minus 5 upon 2. Hence x is equal to minus 5 upon 2 is the zero of Px. Here is I am replacing x by minus 5 by 2 in the polynomial Px we get its value as zero. So this completes the third part and now proceeding on to the fourth part where Px is equal to 3x minus 2. Again here we need to find the value of x such that when x is replaced by the value the value of the polynomial comes out to be zero. So for that we will solve Px is equal to zero or Px is 3x minus 2 is equal to zero. Now on adding 2 both sides we get 3x is equal to 2 or now dividing both sides by 3 to get the value of x we get x is equal to 2 upon 3 since 3 is the common factor of the numerator and denominator. Hence x is equal to 2 upon 3 is the zero of the given polynomial which is 3x minus 2. So this completes the fourth part and now proceeding on to the fifth part where Px is equal to 3x. Here we need to find the value of x such that on replacing x by its value the value of the polynomial comes out to be zero. So we need to solve Px is equal to zero or Px is equal to 3x so 3x is equal to zero. Now I am dividing both left inside and right inside by 3 we get 3x upon 3 is equal to zero upon 3 or 3 cancels out with 3 we have x is equal to zero upon 3 which is equal to zero. Hence x is equal to zero is the zero of the given polynomial Px which is equal to 3x. Now proceeding on to the sixth part where Px is equal to x such that a is not equal to zero. Again we need to find the value of x such that on replacing x by its value we get the value of the polynomial as zero. So for that we will again solve Px is equal to zero and Px is what? Ax so this implies Ax is equal to zero. Now dividing both the left inside and right inside by a we have Ax upon a is equal to zero upon a. Now a cancels out with a so we have x is equal to zero since a is not equal to zero and thus x is equal to zero is the zero of Px. This completes the sixth part and now proceeding on to the last part which is Px is equal to Cx plus D where C is not equal to zero and also C and D are real numbers and the value of x such that the value of the polynomial comes zero on replacing x by that value we will solve x is equal to zero and since Px is equal to Cx plus D so we have Cx plus D is equal to zero or Cx is equal to minus D on adding the negative inverse of D which is minus D on both sides we get Cx is equal to minus D and now on dividing both the left inside and right inside by C we get C cancels out with C, x is equal to minus D upon C thus on replacing x is equal to minus D by C and the polynomial Px we will get the value as zero hence x is equal to minus D upon C is the zero of Px which is the given polynomial. So this completes the last part hence the solution so hope you enjoyed this session take care and have a good day.