Amit and Alok attempted to solve a quadratic equation. Amit made a mistake in writing down the constant term and ended up with roots (4, 3). Alok made a mistake in writing down coefficient of x to get roots (3, 2). The correct roots of the equation are:

Let, the original equation be $$ax^2+bx+c=0$$

So, sum of original roots will be -b/a and product of original roots will be c/a.

Now in the first case, Amit made a mistake in writing down the constant term.

Let, say in that case, the equation he wrote be $$ax^2+bx+d=0$$

Roots of this equation are given as (4,3)

So, sum of roots = -b/a = 4+3 = 7 

or, b =-7a------>(1)

Now, let's pick the second case.

In the second case, he made a mistake in writing down the coefficient of x.

Let, say in that case, the equation he wrote be $$ax^2+ex+c=0$$

Roots of this equation are given as (3,2)

So, product of this roots = c/a = 3*2 = 6 

or, c = 6a------>(2)

Putting the values of b and c in the original equation,

We get the equation as:

$$ax^2-7ax+6a=0$$

or, $$a\left(x^2-7x+6\right)=0$$

Now in a quadratic equation, we know, $$a\ne\ 0$$

So, the original equation is $$x^2-7x+6=0$$

And $$x^2-7x+6=\left(x-1\right)\left(x-6\right)=0$$

So, roots of this equation are 1 and 6

Option (B) 6,1 is the correct answer