Consider the following statements : I. \( \sqrt{x} + x + 1 = 0 \) has two irrational roots. II. \( 5\sqrt{x} - x - 4 = 0 \) has two rational roots. Which of the statements given above is/are correct ?
- A. I only
- B. II only ✓
- C. Both I and II
- D. Neither I nor II
Correct Answer: B. II only
Explanation
Statement I has no real roots because \( \sqrt{x} \) and \( x \) are always non-negative. Statement II simplifies to \( (\sqrt{x} - 1)(\sqrt{x} - 4) = 0 \), giving x=1 and x=16, which are both rational.
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