One of the roots of the quadratic equation x^2-5mx+6m^2=0 is 36. Find the greatest possible value of the second root.

The greatest possible value of the second root will be 54.

Step-by-step explanation:

The given quadratic equation is x² - 5mx + 6m² = 0

So, we have to find the values of variable x.

Now, x² - 5mx + 6m² = 0

⇒ x² - 3mx - 2mx + 6m² = 0

⇒ x (x - 3m) - 2m (x - 3m) = 0

⇒ (x - 3m) (x - 2m) = 0

So, x = 3m and 2m.

Now, if 3m = 36

Then, m = 12 and the other root will be x = 2m = 24.

Again, if 2m = 36

Then, m = 18 and the other root will be x = 3m = 54.

So, if one root of the equation is 36 then, the greatest possible value of the second root will be 54. (Answer)