Let two numbers have arithmetic mean 9 and geometric mean 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
Answers
Answer:
The correct option is C.
Step-by-step explanation:
Let the two number be a, b
(a+b)/2 = 9 and √(ab) = 4
Required equation: x2 - 2(Average value of a, b)x + √(GM)2 = 0
Answer:
X² - 18x + 16
Step-by-step explanation:
Given ---> Arithmetic mean and Geometric mean of two numbers are 9 and 4 respectively.
To find ---> Quadratic equation
Solution---> Let two numbers be a and b
ATQ, Arithmetic mean of number = 9
=> ( a + b) / 2 = 9
=> a + b = 18
ATQ, Geometric mean = 4
√(ab) = 4
Squaring both sides we get
=> {√(ab) }² = ( 4 )²
=> a b = 16
Quadratic equatoin whose roots are given
x² - ( sum of roots ) x + (product of roots ) = 0
ATQ, required equation have roots as a and b,so
=> x² - ( a + b ) x + ( ab ) = 0
Putting a + b = 18 and ab = 16 ,we get
=> x² - ( 18 ) x + ( 16 ) = 0
=> x² - 18 x + 16 = 0
So third option is right ans
Additional information---->
(1) Formula of nth term of GP
aₙ = a rⁿ⁻¹
Where aₙ = nth term of GP
a = First term of GP
r = Common difference
(2) Formula of sum of n terms
Sₙ = a ( rⁿ - 1 ) / ( r - 1 )
(3) Formula of sum of infinite terms
S ( infinite ) = a / ( 1 - r )