Multiple choice

If $ax^{2}+bx+c=0$ is an equation whose sum of roots exceeds 2 but the product of roots is less than 2 .then

  1. $a\left ( b+c \right )< 0$
  2. $\displaystyle b+c< 0$
  3. $\displaystyle a+b+c> 0$
  4. $\displaystyle a+b< 0$
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A Correct answer
Explanation

Sum of roots = -b/a > 2. Product of roots = c/a < 2. For a > 0, -b > 2a => b + 2a < 0. c < 2a. Testing values shows a(b+c) < 0 is the consistent condition.

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