Find the value of K if the following quadratic eq. has real roots.

For the standard quadratic equation to have real roots we must have its discriminant greater than or equal to zero.

Comparing the given equaton, with the standard quadratic equation, we get,

a=1

b= -2 (1+3k)

c=7(3+2k)

So, D=(b*b)-(4*a*c)greater than or equal to zero.

SO,

[4*(1+3K)*(1+3K)]-[4*7*(3+2K)]must be greater than or equal to zero..

solving the inequality we get,