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

Answer 1

Answer:

option (b) is correct

Step-by-step explanation:

$\text{Let the two numbers be a and b}$

$\textbf{Given:}$

$\text{Arithmetic mean=9}$

$\implies\,\frac{a+b}{2}=9$

$\implies\,a+b=18$

$\text{and}$

$\text{Geometric mean=4}$

$\implies\,\sqrt{ab}=4$

$\implies\,ab=16$

$\therefore\text{The quadratic equation having a and b as its roots is }$

$x^2-(a+b)x+ab=0$

$\implies\,\boxed{\bf\,x^2-18x+16=0}$

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Answer 2

Answer:

X2+18x+16=0 this is the answer