Question

If arithmetic mean of two numbers α and β is A and 2α . β = Gthen write a quadratic equation whose roots are α and β​

Answer 1

Let the roots of the quadratic equation be α and β.

Then, the equation is (x  

2

−(α+β)x+αβ=0

∴A=  

2

α+β

​  

 

⇒α+β=2A

g=  

αβ

​  

 

⇒αβ=G  

2

.

Hence, the required equation is x  

2

−2Ax+G  

2

=0.