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Write the quadratic equation, the arithmetic and geometric mea

Question

Write the quadratic equation, the arithmetic and geometric means of whose roots are A and G respectively.

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Text solutionVerified

Let the roots of the quadratic equation be

α

and

β

Then, the equation is

(x^{2} - (α + β) x + α β = 0

∴ A = \frac{α + β}{2}

\Rightarrow α + β = 2 A

g = α β

\Rightarrow α β = G^{2}

Hence, the required equation is

x^{2} - 2 A x + G^{2} = 0

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Question Text	Write the quadratic equation, the arithmetic and geometric means of whose roots are A and G respectively.
Answer Type	Text solution:1
Upvotes	151