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Geometric Mean

State whether...

Question

State whether the following statement is true or false.
If A and G are respectively arithmetic and geometric means between two positive quantities a and b, then the quadratic equation having a, b as its roots is $x^{2} - 2 A x + G^{2} = 0$ .

A

True

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B

False

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Solution

The correct option is A True
We have,
$A = \frac{a + b}{2}$ and $G = \sqrt{a b}$

The equation having a and b as its roots is :
$x^{2} - x (a + b) + a b = 0$ or, $x^{2} - 2 A x + G^{2} = 0$

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