Question

Let the arithmetic mean of two numbers be 9 and the geometric mean be 4, then these numbers are the roots of the quadratic equation___ *

x²+18x+16=0

x²-18x-16=0

x²+18x-16=0

x²-18x+16=0
​

Answer 1

Answer:

x²-18x+16=0

Step-by-step explanation:

Let α and β be two numbers whose arithmetic mean is 9 and the geometric mean is 4.

α+β=18

and αβ=16

(∵AM⇒

2

a+b

andGM⇒ab=c

2

)

Therefore, the required equation is

⇒x

2

−(α+β)x+(αβ)=0

⇒x ^2 −18x+16=0