Let Q = x^2 + bx + c. If the sum of the roots is equal to product of the roots of the equation Q = 0, then which of the following statements is/are correct ? I. Q can be a perfect square. II. Q is positive for all real values of x. Select the answer using the code given below :
- A. I only ✓
- B. II only
- C. Both I and II
- D. Neither I nor II
Correct Answer: A. I only
Explanation
Sum of roots = -b, product = c. Given -b = c, Q = x^2 + bx - b. For Q to be a perfect square, discriminant b^2 - 4(1)(-b) = 0, so b^2 + 4b = 0. If b = 0, Q = x^2 (perfect square). So I is correct. Since Q can be 0, it is not strictly positive for all real x, making II incorrect.
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