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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 x22Ax+G2=0.

A
True
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B
False
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Solution

The correct option is A True
We have,
A=a+b2 and G=ab

The equation having a and b as its roots is :
x2x(a+b)+ab=0 or, x22Ax+G2=0

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