IPMAT Indore 2023 (MCQ) - Let a_1, a_2, a_3 be three distinct real numbers in geometric progression. If the equations a_1 x ^ 2 + 2a_2x + a_3 = 0 and b_1 x ^ 2 + 2b_2x + b_3 = 0 have a common root, then which of the following is necessarily true? | PYQs + Solutions

IPMAT Indore 2023

Algebra

Progression & Series

Medium

Let $a_{1}, a_{2}, a_{3}$ be three distinct real numbers in geometric progression. If the equations $a_{1} x ^ 2 + 2a_{2}x + a_{3} = 0$ and $b_{1} x ^ 2 + 2b_{2}x + b_{3} = 0$ have a common root, then which of the following is necessarily true?

\dfrac{b_{1}}{a_{1}}, \dfrac{b_{2}}{a_{2}}, \dfrac{b_{3}}{a_{3}}

are in geometric progression

b_{1}, b_{2}, b_{3}

are in geometric progression

b_{1}, b_{2}, b_{3}

are in arithmetic progression

\dfrac{b_{1}}{a_{1}}, \dfrac{b_{2}}{a_{2}}, \dfrac{b_{3}}{a_{3}}

are in arithmetic progression

Correct Option: 4