If one of the roots of equation is and one of the roots of the equation is three times the other root, then the value of is
Explanation for the correct option.
Step 1: Prerequisites for the solution.
The quadratic equation is given as then the coefficient of that is is equal to the sum of its roots and the term is equal to the product of its roots.
So, suppose that the roots of the above equation are then and .
Step 2: Calculation for the value of ,
Here, the equation has one of its roots as . Let the other root be then we will get two equations that are,
Here will be negative because the equation will not have real roots otherwise.
From equation , we have
Now, from the equation , we have
Step 3: Calculation for the value of .
We know that the value of is then the second equation will become .
It is given that one root of the equation is three times the other. Suppose that one root is then the other root will be .
Now, the sum of the roots is equal to ,
The other root will be .
Finally is equal to the product of these roots,
Hence, the correct option is (A).