If x is a negative real number, then which of the following are <strong>NOT</strong> correct?<br><br>1. There is some natural number k such that kx \gt 0<br>2. x^{2}+x \gt 0 always<br>3. 2x \lt x \lt -x<br>4. x^{2} is always a rational number<br><br>Select the correct answer using the code given below :
- A. 1, 2 and 3
- B. 1, 2 and 4 ✓
- C. 1, 3 and 4
- D. 2, 3 and 4
Correct Answer: B. 1, 2 and 4
Explanation
For x \lt 0: Statement 1 is false because natural numbers are positive, making kx \lt 0. Statement 2 is false as x^2+x is negative for x = -0.5. Statement 4 is false if x is an irrational number like -\sqrt{2}. Only Statement 3 is true.
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