 Hey friends, welcome again. So I am hopeful that all of you are liking these videos and we have covered a significant portion so far. We have seen what quadratic equations are and you know, what are the methods of solving quadratic equations. And in the last session, we discussed about the nature of roots of quadratic equation. So this particular session is based on the previous one only and we are trying to solve a few questions based on the concepts which we learned in the last few sessions. Now the question here is, determine the nature of the roots of the following quadratic equations, right? So we learned three cases in the last, you know, session and now we are going to apply them. And just to have a quick recap, what did we discuss last time? We discussed that there are three cases, this one, when discriminant that is b square minus 4ac of any quadratic equation is greater than 0, then we have two distinct, two distinct real roots, real roots, that was the nature of the roots and then case two was when d is equal to 0, then we said two equal real roots, two equal real roots, that means roots are real but they are same, they are equal and third was if d is less than 0, then we have two non-real or complex roots, right? This is what we learned so far. So now we are going to apply this concept. So please keep this in mind and let's see how we can find out the nature of roots for this particular given equation, right? So you know now in the first case, a is 2, so a is 2, b is 1 and c is minus 1, isn't it? So this is the value of a, b and c in the case, in the first case, so hence let's calculate b square minus 4ac, that is discriminant d is equal to b square minus 4ac which is nothing but 1 square, so b is 1 and minus 4 times 2 times minus 1 which is clearly 1 plus 8 which is 9 which is clearly greater than 0, so hence we get case 1, case 1 that is in this case d is greater than 0, so we will be having two distinct, distinct means two different. So in this case it will be two distinct real roots, okay? Now one thing you can notice here, what is to be noticed if you see if any of a and c is negative, guys, if any of a and c is negative then the roots will definitely be real, you understand? So if any of a and c, only one but if a and c are of or if a and c are of opposite signs, opposite signs, if a and c are of opposite signs then clearly b square minus 4ac will be always greater than 0, isn't it? Why? Because if a and c are opposite sign then a and c is negative and if a and c is negative then minus 4ac is positive, so hence it will always be greater than 0, right? So this is a good trick to remember, if a either of a and c or basically if a and c are of opposite signs then the roots are real, correct? Now let's go to the second question, the second question says, the second question is 2x square 2x square plus 5x plus 5 is equal to 0, this is the equation. Now clearly if you see a and c are of same signs so we'll have to check the discriminant, a is 2, b is 5 and c is also 5, so let's find out discriminant value, so discriminant value d is b square minus 4ac which is equal to 5 square minus 4 times 2 times 5 is equal to 25 minus 40, right? Which is minus 15, correct? Which is less than 0, so hence if it is less than 0 you know what is it? Case 3, case 3 is 2 non real roots are there, non real roots, 2 non real roots, okay? Sorry you can say the roots, real roots do not exist, real roots do not, do not exist. This is how, it's very simple, you have to just remember this formula, this is a crucial formula, so hence, so d is equal to b square minus 4ac, if you remember this, find this, greater than 0, 2 distinct real roots equal to 0, equal roots and less than 0, non real roots, okay? This is how you have to solve these kind of problems.