Verified answer

4x^2 - mx + 5 = 0

Let one root be a and the other be 3a.

Using Viete's formulas,

a + 3a = m/4

-> 16a = m

a*3a = 5/4

-> 12a^2 = 5

-> a^2 = 5/12

-> a = √(5/12)

m = 16a = 16√(5/12) = 8√(5/3)

eqn 4x^2 = mx -- 5 has roots in the ratio 3 : 1 whence

5/4 = 3a^2 = 3(m/16)^2 Or m^2 = 5*256/12 = 320/3 Or m = +/-- 8sqrt(5/3)

4x² = mx - 5

- 4x² + mx = 5

4x(- x + m) = 5

- x + m = 5/4x

m = 5/4x + x

m = 5/4x + 4/4x

m = 9/4x or 3(3/4x) or x([3/2]²)