 Hi and welcome to the session I am Deepika here. Let's discuss the question, find the nature of the rules of the following quadratic equation if the real roots exist, find them. 2x square minus 3x plus 5 is equal to 0. Now we know that the roots of the quadratic equation here plus bx plus c is equal to 0 are given by x is equal to minus b plus minus under root of b square minus 4ac upon 2a. Now since b square minus 4ac determines whether the quadratic equation ax square plus bx plus c is equal to 0 has real roots or not and b square minus 4ac is called the discriminant of the quadratic equation. Now a quadratic equation here plus bx plus c is equal to 0 has number one two distinct real roots if b square minus 4ac is greater than 0 that is discriminant is greater than 0. Number two quadratic equation ax square plus bx plus c is equal to 0 has two equal roots if b square minus 4ac is equal to 0 third no real roots exist if discriminant that is b square minus 4ac is less than 0. So this is the key idea behind our question we will take the help of this key idea to solve above question. So let's start the solution given quadratic equation is x square minus 3x plus 5 is equal to 0 on comparing with quadratic equation ax square plus bx plus c is equal to 0 we have is equal to 2 b is equal to minus 3 c is equal to 5 therefore the discriminant b square minus 4ac is equal to minus c square minus 4 into 2 into 5 and this is equal to 9 minus 40 and this is equal to minus 31. Since b square minus 4ac that is discriminant is less than 0 hence according to the key idea the given quadratic equation has no real roots the answer for the above question is real roots do not exist I hope the solution is clear to you buy and take care