The difference between two roots of the equation is . Then, the roots of the equation are
Explanation for the correct option :
Step 1 : Constructing a system of three equations
Given : Difference between two roots of is
Let and be the roots of the given equation .
Formula to be used : We know that if be the roots of the equation , then,
.
Here, the given equation is and the roots are and . So, we get the following three equation:
Applying the values in equation
Applying the values in equation
Applying the values in equation
Step 2 : Solving the equations using the substitution method
From the equation , we get . Substituting this in equation , we get :
This implies either or .
Step 3: Finding the roots
When ,
Then the three roots will be .
When ,
and
Then, the three roots will be .
Hence, option (A) is the correct answer.