Complex Numbers And Quadratic Equations question 615
Question: Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation [AIEEE 2004]
Options:
A) $ x^{2}-18x-16=0 $
B) $ x^{2}-18x+16=0 $
C) $ x^{2}+18x-16=0 $
D) $ x^{2}+18x+16=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
Let the two number is $ x_1 $ and $ x_2 $ $ \frac{x_1+x_2}{2}=9 $ and $ x_1x_2=16 $ $ x_1+x_2=18 $ and $ x_1x_2=16 $ . Equation $ x^{2}-(\text{Sum of roots)}x+\text{Product of roots}=0 $ Required equation $ x^{2}-18x+16=0 $ .
BETA
