 Hello friends, welcome to the session and we are going to find the roots of quadratic equation given in question number first above by applying the quadratic formula. Our equation is 2x square minus 5x plus 3 equal to 0. Before starting with the solution, I would like to tell you the basic idea behind the question. If ax square plus bx plus c equal to 0 where a is not equal to 0 is a quadratic equation then d equal to b square minus 4ac where d is discriminant and its roots are given by alpha equal to minus b plus square root of d upon 2a and beta equal to minus b minus square root of d upon 2a. Now, let's start with the solution. Now on comparing 2x square minus 7x plus 3 equal to 0 with ax square plus b plus 3 equal to 0 we have a equal to 2b equal to minus 7 and c equal to 3 therefore d equal to b square minus 4ac or it can be written as minus 7 square minus 4 into 2 into 3. This implies d equal to 49 minus 24 or d equal to 25 therefore the roots are alpha equal to minus b plus square root of d by 2a this can be written as alpha equal to minus of minus 7 plus square root of 25 by 2 into 2 or this can be written as plus 7 plus 5 upon 4 which gives us 12 upon 4 on cancelling we get 3 this implies alpha equal to 3. Similarly, we calculate beta beta equal to minus b minus square root of d upon 2a it can be written as minus of minus 7 minus square root of 25 upon 2 into 2 this gives plus 7 minus 5 upon 4 or this can be written as 2 upon 4 this implies beta equal to 1 by 2 therefore the roots are 3 and 1 by 2 hope you understood the solution and enjoyed the session goodbye and take care