IPMAT Question Paper 2023 | IPM Indore Quantitative Ability

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Question 34 :Let $a_1, a_2, a_3$ be three distinct real nubers in geometric progression. If the eqations $a_1 x^2+2 a_2 x+$ $a_3=0$ and $b_1 x^2+2 b_2 x+b_3+=0$ have a common root, then which of the following is necessarily ture?

1. $\frac{b_1}{a_1}, \frac{b_2}{a_2}, \frac{b_3}{a_3}$ are in arithmetic progression
2. $b _1, b_2, b_3$ are in arithmetic progression
3. $\frac{b_1}{a_1}, \frac{b_2}{a_2}, \frac{b_3}{a_3}$ are in geometric progression
4. $b _1, b_2, b_3$ are in geometric progression

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Explanatory Answer

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The question is "Let $a_1, a_2, a_3$ be three distinct real nubers in geometric progression. If the eqations $a_1 x^2+2 a_2 x+$ $a_3=0$ and $b_1 x^2+2 b_2 x+b_3+=0$ have a common root, then which of the following is necessarily ture?"

Hence, the answer is '$\frac{b_1}{a_1}, \frac{b_2}{a_2}, \frac{b_3}{a_3}$ are in arithmetic progression'

 

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