Multiple choice

If $C > 0$ and the equation $3 a x ^ { 2 } + 4 b x + c = 0$ has no real root, then

  1. $2 a + c > b$
  2. $a + 2 c > b$
  3. $3 a + c > 4 b$
  4. $a + 3 c < b$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For no real roots, discriminant D < 0. D = (4b)^2 - 4(3a)(c) = 16b^2 - 12ac < 0. 4b^2 < 3ac. Since c > 0, this implies a must be positive. The inequality 3a + c > 4b is a standard property derived from the quadratic condition.

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