 Hello and welcome to the session. In this session we will discuss the equation which says that for what values of k will the equation 9x squared plus kx plus 1 is equal to 0 have real and equal roots. Now before starting the solution of this question, we should know a result. Now the standard form of quadratic equation is ax squared plus bx plus c is equal to 0. Where a is not equal to 0 and abc are the constants. Now the nature of the roots depends entirely on the value of the expression b squared minus 4ac which is also called discriminant and it is denoted by the letter d. Now if b squared minus 4ac is equal to 0 then the roots of the equation are real and equal. Now this result will work out as a key idea for solving out this question. And now we will start with the solution. Here the equation is given as 9x squared plus kx plus 1 is equal to 0. Now comparing this equation with the standard form of quadratic equation here, a is equal to 9, b is equal to k and c is equal to 1. Now in the question it is given that the equation is having real and equal roots. Now we know that when b squared minus 4ac is equal to 0 then the roots of the equation are real and equal. So we can write since the roots are real and equal therefore d squared minus 4ac is equal to 0. This implies by putting the values of b, a and c here it will be k squared minus 4 into 9 into 1 is equal to 0. Which implies k squared minus 36 is equal to 0. This implies k squared is equal to 36 which implies k is equal to square root of 36. This implies k is equal to plus minus 6. Therefore the required value of kr plus 6 and minus 6. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed the session.