Question

If12 and 9 are respectively A.M and G.M of
two numbers, then the numbers are
the roots of the equation
Select one:
O a. x2
24x + 81 = 0
b. x2 - 81x + 24 = 0
c. x2 + 81x + 24 = 0
d. x2 7 24x - 81 = 0
Clear my choice​

Answer 1

$\textbf{Given:}$

$\textsf{A.M and G.M of two numbers are 12 and 9}$

$\textbf{To find:}$

$\textsf{The quadratic equation whose roots are having A.M=12 and G.M=9}$

$\textbf{Solution:}$

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

$\mathsf{A.M=12}$

$\implies\mathsf{\dfrac{a+b}{2}=12}$

$\implies\boxed{\mathsf{a+b=24}}$

$\mathsf{and}$

$\mathsf{G.M=9}$

$\implies\mathsf{\sqrt{ab}=9}$

$\implies\boxed{\mathsf{ab=81}}$

$\therefore\textsf{The required quadratic equation is }$

$\mathsf{x^2-(a+b)x+ab=0}$

$\mathsf{x^2-(24)x+81=0}$

$\implies\boxed{\mathsf{x^2-24\,x+81=0}}$

$\textbf{Answer:}$

$\textsf{Option (a) is correct}$

$\textbf{Find more:}}$

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

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