Q. Consider the following statements: 1. The equation $x^{2} - cx + d = 0\ and\ x^{2} - ax + b = 0$ have common root and second equation has equal roots if $ac = 2(b + d)$. 2. If $\alpha$ is a root of the equation $4x^{2} + 2x - 1 = 0$, then the other root is $4\alpha^{3} - 3\alpha$. 3. The expression $(x - 1)(x - 3)(x - 4)(x - 6) + 10$ is positive for all real values of $x$. Which of these is/are correct?
A) Only (3)
B) Only (2)
C) All of these
D) None of these
Explanation
The correct answer is Option C: All of these.
A detailed explanation for this question is being prepared.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.