Multiple choice

Directions: The given question is followed by two statements I and II. You have to identify which statements are sufficient to answer the question and mark the appropriate option. What is the sum of roots of equation 5cx2 + (a + b)x + 1 = 0? I. a + c = 0 II. 3a + 2b + c = 5

  1. Only statement I alone is sufficient to answer the question.

  2. Only statement II alone is sufficient to answer the question.

  3. Both the statements together are sufficient to answer the question.

  4. Both the statements together are insufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of roots = -(a+b) / (5c). We have two equations with three variables (a, b, c). Statement I: a = -c. Statement II: 3a + 2b + c = 5. Even with both, we cannot determine the ratio (a+b)/c uniquely.

AI explanation

The sum of roots of the quadratic equation 5cx^2 + (a + b)x + 1 = 0 is given by -(a + b)/(5c). Statement I provides a + c = 0, and statement II provides 3a + 2b + c = 5. Even by combining and solving these two linear equations, we get a relationship like 2a + b = 5, but the individual values of variables a, b and c remain unknown. Therefore, the exact value of the sum of roots cannot be determined.

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