Multiple choice

If both roots of the equation $ g (x) = 0 $ are greater than $-1,$ then sum of roots lies in the interval :

  1. $ ( - \infty , -2 ) $
  2. $ \left( - \infty , \dfrac {-1}{4} \right)$
  3. $ ( -2,  \infty ) $
  4. $ \left( \dfrac {-1}{2} , \infty\right)$
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C Correct answer
Explanation

If roots r1, r2 > -1, then (r1+1) > 0 and (r2+1) > 0. Sum of roots = r1+r2. Since r1 > -1 and r2 > -1, r1+r2 > -2. Thus the sum lies in (-2, infinity).

AI explanation

Let the roots of the equation be m and n. Since both roots are strictly greater than -1, we have m > -1 and n > -1. Adding these two inequalities together yields m + n > -2. The sum of the roots therefore lies in the interval (-2, infinity). The result is (-2, infinity).

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