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. 100PTS!

The greatest possible value is 54

Step-by-step explanation:

Solve the quadratic equation

Given

x² - 5mx + 6m² = 0

We can rewrite this as

x² - 3mx - 2mx + 6m² = 0

(x² - 3mx) - (2mx - 6m²) = 0

x (x - 3m) - 2m (x - 3m) = 0

(x - 2m) (x - 3m) = 0

x - 2m = 0 or x - 3m = 0

So,

x = 2m or x = 3m.

2m and 3m are the roots of the equation.

Since one of the roots is 36

Assume

2m = 36

m = 36/2 = 18

3m is

3 (18) = 54

If 3m = 36

m = 12

And

2m = 2 (12) = 24.

The greatest possible value is 54