Given equation is \( \Large 7x^{2}-50x+k=0 \)

Here, a = 7, b = -50, c = k

Since, \( \Large \alpha + \beta =\frac{-b}{a} \)

Therefore, \( \Large \alpha + \beta =\frac{50}{7} \)

or \( \Large \beta =\frac{50}{7}-7 \)

=> \( \Large \beta =\frac{1}{7} \) [Because \( \Large \alpha = 7 \)(given)]

and \( \Large \alpha \beta =\frac{c}{a} \)

or \( \Large 7 \times \frac{1}{7}=\frac{k}{7} \)

k = 7