 Okay, so in this question, it's given that if x equals to 2 and x equals to 3 are roots of equation, which equation? 3x square minus 2kx plus 2m equals 0. We have to find out the value of k and m. Okay, so basically roots are given, values are given, we have to find out unknowns k and m. So what is meant by x and x equals 2 and x equals to 3 being the roots of this equation? That means if we deploy x equals to 2 in this equation, if you put x equals to 2 in this equation, you should get LHS equal to RHS. So let's do that. So it is 3 times 2 square minus 2 times k, k is unknown, times 2, x is 2, we are taking it and 2m equals 0, isn't it? So hence it is 3 times 4, which is nothing but 12, right? Minus 4k plus 2m is equal to 0. So if you see, we can eliminate a 2 from the entire equation and you will get 2 gets cancelled. So 6 minus 2k plus m equals 0. Simplifying I can write 2k minus m equals 6. Correct? This is first equation. Secondly, you can see x equals to 3 also is a solution. So hence instead of x, you can write 3 as well. So 3 into 3 square. So I am plugging in x equals 3. Wherever there is x, you have to simply replace it by 3 and simplify. Plus 2m equals 0. So hence 3 times 9 is 27 minus 6k minus 6k and plus 2m equals 0. So hence you will get 2m minus 6k, 2m minus 6k or rather 6k minus 2m. Let me write it like that. So I am writing 6k minus 2m for simplicity sake. 6k minus 2m is equal to 27. Now this is equation number 1 and this is equation number 2. So if you solve these linear equations, if you see this is nothing but linear equation in k and m, sorry this is not x, this is k here. So this is simply 6k, 6k minus 2m equals 27. Now let us solve these. So you know how to solve a linear equation in 2 variable. You can directly substitute or eliminate whichever way. So from here I can say m is equal to 2k minus 6. Just manipulating it, m is equal to 2k minus 6. And now let us deploy this value of m here. So what will you get? You will get 6k minus 2 times m. m is 2k minus 6 from this relation 3. Okay? And this equals 27. So let us simplify. 6k minus 4k plus 12, isn't it? Is equal to 27. So 2k is equal to 27 minus 12. So k is equal to 15 upon 2. This is the value of k. And from 3 you can say, from equation 3, what can you say? m is equal to 2k minus 6. So hence it is 2 times k. k we just found out is 15 upon 2 minus 6. So hence 15 minus 6, which is 9. This 2 and this 2 goes, right? 15 minus 6 is 9. So hence if we know the roots of an equation, we can find out other unknowns given in the equation, right? This is what is the learning from this solved example.