Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

Question

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation (A) x2 + 18x + 16 = 0 (B) x2 −18x −16 = 0 (C) x2 + 18x −16 = 0 (D) x2 −18x + 16 = 0

Tardigrade Admin · Accepted Answer

Let numbers be a, b ⇒ a + b = 18, √ab = 4 ⇒ ab = 16 , a and b are roots of the equation ⇒ x2 −18x + 16 = 0 .

Q. Let two numbers have arithmetic mean $9$ and geometric mean $4$ . Then these numbers are the roots of the quadratic equation

$x^{2} + 18 x + 16 = 0$

$x^{2} - 18 x - 16 = 0$

$x^{2} + 18 x - 16 = 0$

$x^{2} - 18 x + 16 = 0$

Let numbers be $a, b \Rightarrow a + b = 18, ab = 4 \Rightarrow ab = 16,$ a and b are roots of the equation
$\Rightarrow x^{2} - 18 x + 16 = 0.$

Q. 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