If the arithmetic mean and the geometric mean of two numbers a and b are denoted by A and G respectively then form a quadratic equation whose roots are a and b.
Answer & explanation
Correct answer: option 4
a, b, be roots of equation, so equation is
x2−(a+b)x+αβ=0
Here,
(a+b)/2=A
a+b=2A
And √a = G
√ab = G
av = G2
So,
Required equation is,
x2−2Ax+G2= 0