Question

Write a quadratic equation with 7 and 2/5 as its roots. Write the equation in the form ax2 + bx+c= 0, where a, b, and c are integers.

Answer 1

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,

$\begin{gathered} b=-((7)+(\frac{2}{5})) \\ b=-(\frac{35+2}{5}) \\ b=-\frac{37}{5} \end{gathered}$

And

c is the products of the roots

So,

$\begin{gathered} c=7\times\frac{2}{5} \\ c=\frac{14}{5} \end{gathered}$

Now,

The desired quadratic equation is:

$\begin{gathered} ax^2+bx+c=0 \\ x^2-\frac{37}{5}x+\frac{14}{5}=0 \\ 5x^2-37x+14=0 \end{gathered}$

Hence, the correct option is A.