 Hello friends welcome to the session. I am Alka today We are going to find the roots of the following quadratic equations if they exist by the matter of completing the square Our given equation is 4x square plus 4 root 3x plus 3 equal to 0 Let's start with the solution now on dividing both the sides of the given equation by 4 we get x square plus 4 root 3x upon 4 Plus 3 by 4 equal to 0 this implies x square plus 4 root 3 x by 4 4 4 cancel out equal to minus 3 by 4 We have shifted the constant term to LHS this can be written as x square plus 2 root 3 by 2x plus root 3 by 2 whole square equal to minus 3 by 4 plus root 3 by 2 Whole square we have added root 3 by 2 whole square on both the sides This can be written as x plus root 3 by 2 Whole square equal to minus 3 by 4 plus 3 by 4 This implies x plus root 3 by 2 whole square equal to 0 Now on taking square root on both the sides we get x plus root 3 by 2 equal to 0 This implies x equal to minus square root of 3 by 2 therefore x equal to minus square root of 3 by 2 minus square root of 3 by 2 Hence the roots are minus root 3 by 2 and minus root 3 by 2 which is a required answer Hope you understood the solution and enjoyed the session. Goodbye and take care