Find the roots of 2x² − 5x + 3

We have to factorise 2x²−5x+3=0

We will use splitting the middle term method

Split the middle term by finding two numbers (-2 and -3) such that their sum is equal to the coefficient of x and their product is equal to the product of the coefficient of x2 and the constant.
2x²−2x−3x+3=0
=2x²−2x−3x+3=0
=2x(x−1)−3(x−1)=0
=(x−1)(2x−3)=0

Thus, x = 1 and x =3/2 are the roots of the given quadratic equation.