What is the value of m which satisfies 3m^2 - 21m + 30

What is the value of m which satisfies 3m2 - 21m + 30 < 0?

  1. m < 2 or m > 5; 2 < m < 5
  2. 2 < m < 5
  3. m < 2 or m > 5
  4. m > 2

Answer

3m2 - 21m + 30 < 0

3m2 - 6m - 15m + 30 < 0

3m(m - 2) - 15(m - 2) < 0

(m - 2)(3m - 15) < 0

Case 1: (m - 2) > 0 and (3m - 15) < 0

m > 2 and m < 5

Case 2: (m - 2) < 0 and (3m - 15) > 0

m < 2 and m > 5

The correct option is A.