Hi Harish,
at a first glance it might be tempting to choose C, since in principle quadratic equations give you two possible solutions, and therefore one answer choice would not be sufficient.
Let's first take a look statement (1):
(1) If you factorize the quadratic expression (see here for a good explanation of factoring quadratics:
https://www.purplemath.com/modules/factquad.htm), you get:
\(3x^2-8x-35=(x-5)(3x+7)\)
from this, it follows: \(x=5\) OR \(\frac{7}{3}\), therefore (1) is NOT SUFFICIENT
A logical approach now, but it would be misleading, would be to check whether statement (2) leads you to any of the two solutions you just found. To do this we just have to plug in \(5\) and \(x=-\frac{7}{3}\) and see if the result is zero. If we do this, we find that \(5\) does in fact work, and we could be tempted to choose C. #FAIL!!!!
This is a good example of why it's important to look at each statement separately. If we solve the quadratic expression from statement (2), we'll quickly see that this equation has a unique (double) solution, which is 5. Therefore B is the right answer!!
Hope this helps!
Cheers.
paula