2023 - 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

Algebra

Medium

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

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