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)+((2)/(5))) \\ b=-((35+2)/(5)) \\ b=-(37)/(5) \end{gathered}`

And

c is the products of the roots

So,

`\begin{gathered} c=7*(2)/(5) \\ c=(14)/(5) \end{gathered}`

Now,

The desired quadratic equation is:

`\begin{gathered} ax^2+bx+c=0 \\ x^2-(37)/(5)x+(14)/(5)=0 \\ 5x^2-37x+14=0 \end{gathered}`

Hence, the correct option is A.