As given by the question
There are given that the roots: 7 and 2/5.
Now,
Since the roots are integers, we can write the equation in the given form using a = 1.
Then,
b is the opposite of the sum of the roots
So,
[tex]\begin{gathered} b=-((7)+(\frac{2}{5})) \\ b=-(\frac{35+2}{5}) \\ b=-\frac{37}{5} \end{gathered}[/tex]And
c is the products of the roots
So,
[tex]\begin{gathered} c=7\times\frac{2}{5} \\ c=\frac{14}{5} \end{gathered}[/tex]Now,
The desired quadratic equation is:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x^2-\frac{37}{5}x+\frac{14}{5}=0 \\ 5x^2-37x+14=0 \end{gathered}[/tex]Hence, the correct option is A.