Multiple choice

All roots of the equation m4 - 8m3 + bm2 - cm + 16 = 0 are real where b and c are constants. What is the maximum possible value of b + c?

  1. 24

  2. 38

  3. 42

  4. 56

  5. 64
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a quartic with real roots, we look at the product of roots (16). If all roots are 2, the equation is (m-2)^4 = m^4 - 8m^3 + 24m^2 - 32m + 16 = 0. Here b=24, c=32. b+c = 56. This satisfies the condition for real roots.

Keep practicing — related questions