 Hello friends welcome to this session on polynomials and we are going through the Problems related to zero of a polynomial So in the last session we learned what a zero of a polynomial is zero of a polynomial is the value of the variable Which makes the value of the or which reduces the value of the polynomial to zero, right? That is what we learned now here is the question which asks you to prove that or show that a Given value of the variable that is in this case x equals to one is a root of the polynomial or The zero so we did not mention last time zero zeroes are also called roots The name is root so root or zero are interchangeably used So the question is show that x equals to one is a root of the polynomial 2x cube minus 2x square plus 6x minus 6 Okay, how to prove this or how to show that The x equals to one is a root or you know Zero of a polynomial. So basically what did we learn we learned that if so this is a solution so if x equals to a is a zero or Root now we know another name root of a polynomial of a polynomial poly normal then Polynomel which polynomial px. Let's say px then P of a is zero That is what we learned so that means if in this case x is x equals to one is a root of this polynomial Then let's find out Let's find out P1 Right px equals to one So what if what is the value of px if x equals to one? So this will be simply 2 Into 1 to the power 3 minus 2 into 1 squared Plus 6 times 1 minus 6 Isn't it so you have to simply substitute x by 1 ok so let's find the value This is 2 minus 2 plus 6 minus 6 and hence This is indeed 0 so since P1 is 0 so we can write since P1 Since P1 is 0 therefore 1 or x equals to 1. Let's write it like that x equals to 1 x equals to 1 Is the 0 root of px Hope you understood this right. Let's take another example. So in this example We have to show that x equals to 3 is a root of the polynomial px equals x square minus 7x plus 12 Let's try to show that how to do that. You know already now So what you need to do is you have to simply find out p of 3 and Check whether it is coming out to be 0 if p3 is 0 then 3 is the 0 or the root of the polynomial Px so what is p3 folks p3 is 3 squared minus 7 times 3 Plus 12 isn't it? simply deploy x equals to 3 or substitute x by 3. So what is this 9 minus 21 plus 12 Indeed it is 0 right therefore P Since p3 is 0. So you should you should write since since P of 3 is 0 therefore x equals to 3 is a 0 of or root of Px Okay, so with these two examples I think now it's clear how to find out or how to show whether some variable value is the root of a given polynomial