Suppose the equations $$3x^{2} — 7x + k = 0$$ and $$—7x^{2} + kx + 3 = 0$$ have a common root, then the value of $$k$$ is:

The simplest way to solve this question would be through the options. 

Option A: $$3x^{2} — 7x + k = 0$$ and $$—7x^{2} + kx + 3 = 0$$ on putting k= 3 becomes, 
$$3x^{2} — 7x + 3 = 0$$ and $$—7x^{2} + 3x + 3 = 0$$
Where we can not calculate the roots by factorisation. 

Option B: $$3x^{2} — 7x + k = 0$$ and $$—7x^{2} + kx + 3 = 0$$ on putting k= 6 becomes, 
$$3x^{2} — 7x + 6 = 0$$ and $$—7x^{2} + 6x + 3 = 0$$
Where again,we can not calculate the roots by factorisation.

Option C: $$3x^{2} — 7x + k = 0$$ and $$—7x^{2} + kx + 3 = 0$$ on putting k= 4 becomes, 
$$3x^{2} — 7x + 4 = 0$$ and $$—7x^{2} + 4x + 3 = 0$$
Where the first equation has roots 1 and 4/3 and the second equation has roots 1 and 3/7

Option D: $$3x^{2} — 7x + k = 0$$ and $$—7x^{2} + kx + 3 = 0$$ on putting k = 2 becomes, 
$$3x^{2} — 7x + 2 = 0$$ and $$—7x^{2} + 2x + 3 = 0$$
Where the first equation has roots 2 and 1/3 but for the second equation, we can not calculate the roots by factorisation.


We can see that option C gives us one common root, hence, that would be our answer.