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The quadratic in t, such that AM of its roots is A and GM is G is:

A) \( \Large t^{2}-2At+G^{2}=0 \)
B) \( \Large t^{2}-2At-G^{2}=0 \)
C) \( \Large t^{2}+2At+G^{2}=0 \)
D) none of these.

Correct Answer:

A) \( \Large t^{2}-2At+G^{2}=0 \)

Description for Correct answer:

Let \( \Large \alpha \), \( \Large \beta \) are the root of the required equation,

then \( \Large A = \frac{ \alpha + \beta }{2} => \alpha \beta = 2A \)

and \( \Large G=\sqrt{ \alpha \beta } => \alpha \beta = G^{2} \)

the required equation is \( \Large t^{2}-2At+G^{2}=0 \)

Part of solved Quadratic Equations questions and answers : >> Elementary Mathematics >> Quadratic Equations

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Similar Questions

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