Q. Consider the following statements: 1. If the ratio of roots of the quadratic equation $ax^{2} + bx + c = 0$ be $p:q,$ then $p{qb}^{2} = (p + q)^{2}ac.$ 2. If the roots of $ax^{2} + bx + c = 0\ are\ \alpha\ and\ \beta,$ then the roots of $cx^{2} + bx + a = 0\ will\ be\frac{1}{\alpha},\ \beta$. 3. The roots of the equation $ax^{2} + bx + c = 0$ are reciprocal to $a^{'}x^{2} + b^{'}x + c^{'} = 0$, if $\left( cc^{'} - aa^{'} \right)^{2} = \left( ba^{'} - cb^{'} \right)(ab^{'} - bc^{'})$. Which of the statements given above are correct?
A) (1) and (2)
B) (2) and (3)
C) (1) and (3)
D) All (1), (2) and (3)
Explanation
The correct answer is Option C: (1) and (3).
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.