(B) Let the two numbers be $a$ and $b$.Given that the arithmetic mean is $\frac{a + b}{2} = 9$,so $a + b = 18$.Given that the geometric mean is $\sqrt

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(B) Let the two numbers be $a$ and $b$.Given that the arithmetic mean is $\frac{a + b}{2} = 9$,so $a + b = 18$.Given that the geometric mean is $\sqrt{ab} = 4$,so $ab = 16$.The quadratic equation whose roots are $a$ and $b$ is given by $x^2 - (a + b)x + ab = 0$.Substituting the values,we get $x^2 - 18x + 16 = 0$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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Consider two numbers whose arithmetic mean is $9$ and geometric mean is $4$. These numbers are the roots of which equation?

A
$x^2 + 18x - 16 = 0$
B
$x^2 - 18x + 16 = 0$
C
$x^2 + 18x + 16 = 0$
D
$x^2 - 18x - 16 = 0$

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4-2.Quadratic Equations and Inequations

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Consider two numbers whose arithmetic mean is $9$ and geometric mean is $4$. These numbers are the roots of which equation?

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