Suppose the equations 3x² - 7x + k = 0 and -7x² + kx + 3 = 0 have a common root, then the value of K is:

Let the common root be r. 3r^2 - 7r + k = 0 and -7r^2 + kr + 3 = 0. Multiply first by 7 and second by 3: 21r^2 - 49r + 7k = 0 and -21r^2 + 3kr + 9 = 0. Adding them: (3k - 49)r + (7k + 9) = 0. r = -(7k+9)/(3k-49). This is complex. Alternatively, test options: If k=4, 3x^2 - 7x + 4 = 0 -> (3x-4)(x-1)=0, roots 4/3, 1. -7x^2 + 4x + 3 = 0 -> -(7x+3)(x-1)=0, roots -3/7, 1. Common root is 1.