 Hello and how are you all doing today? My name is Priyanka and let us discuss this question. It says find the values of k for which the given equation has real and equal roots. Now the equation which is given to us is 12x squared plus 4kx plus 3 is equal to 0. Let us start with our solution. Now we know that for real roots, discriminant should be equal to 0. That is the value of b square minus 4ac should be equal to 0. Now here the given equation is 12x square plus 4kx plus 3 is equal to 0. Here the values of b which we will be taking here are 12, 4k and 3 respectively. So therefore we have b square that is 4k the whole square minus 4a into c equal to 0. This implies 16k square minus minus 144 that is the product of 4, 12 and 3 is equal to 0 which further implies 16k square is equal to 144. k square is equal to 144 divided by 16. k square is equal to 9. So we have the value of k at under root 9 that is plus minus 3. So this is the required answer to the given question. So hope you understood the whole concept well and enjoyed it too. Have a nice day ahead.