JEE MAIN - Mathematics (2004 - No. 34)
Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation
$${x^2} - 18x - 16 = 0$$
$${x^2} - 18x + 16 = 0$$
$${x^2} + 18x - 16 = 0$$
$${x^2} + 18x + 16 = 0$$
Explanation
Let two numbers be a and b then $${{a + b} \over 2} = 9$$
and $$\sqrt {ab} = 4$$
$$\therefore$$ Equation with roots $$a$$ and $$b$$ is
$${x^2} - \left( {a + b} \right)x + ab = 0$$
$$ \Rightarrow {x^2} - 18x + 16 = 0$$
and $$\sqrt {ab} = 4$$
$$\therefore$$ Equation with roots $$a$$ and $$b$$ is
$${x^2} - \left( {a + b} \right)x + ab = 0$$
$$ \Rightarrow {x^2} - 18x + 16 = 0$$
Comments (0)
