 Hello friends, welcome to the session. I am Malka. Today we are going to find the roots of quadratic equations given in question first above by applying the quadratic formula. Our equation is 4x squared plus 4 root 3x plus 3 equal to 0. Now, let's start with the solution. Our given equation is 4x squared plus 4 root 3x plus 3 equal to 0. Now we compare our given equation with ax squared plus bx plus c equal to 0 and we have a equal to 4, v equal to 4 root 3 and c equal to 3. Now we can calculate the value of d. Therefore, d equal to b square minus 4ac. This gives us d equal to 4 root square of 4 root 3 minus 4 into 4 into 3 which is equal to 48 minus 48. This implies d is equal to 0. Now the roots are alpha equal to minus v plus square root of d upon 2a and beta equal to minus b minus square root of d upon 2a. Alpha equal to minus 4 root 3 plus 0 upon 2 into 4. This gives alpha equal to minus 4 root 3 upon 8. On cancelling it, we get alpha equal to minus root 3 by 2. Similarly for beta, we see beta equal to minus 4 root 3 minus 0 upon 2 into 4. This gives beta equal to minus 4 root 3 upon 8. This implies beta equal to minus root 3 by 2. Hence the roots are minus root 3 by 2 and minus root 3 by 2 which is a required solution. Hope you understood it and enjoyed the session. Goodbye and take care.