 Hello friends, welcome to the session. I am Malka and today we are going to find the roots of the following quadratic equation If they exist by the matter of completing the square our equation is 2x square plus x plus 4 equal to 0 Now let's start with the solution Let's start with the solution now on dividing the equation by 2 we get x square plus x by 2 plus 4 by 2 equal to 0. In the next step this implies x square plus x by 2 equal to minus 2 This implies x square plus 2 into 1 by 4 x plus 1 by 16 equal to minus 2 plus 1 by 16 This implies x plus 1 whole square equal to minus 32 plus 1 by 16 This implies x plus 1 by 4 whole square equal to minus 31 by 16 now We see that RHS is Negative, but x plus 1 whole square cannot be negative for any real value of x So the roots of the given equation does not exist Hope you understood the solution and enjoyed the session. Goodbye and take care