First slide

Theory of expressions

Question

The product of the roots of the equation, $9 x^{2} - 18 |x| + 5 = 0$ is

Easy

A

$\frac{25}{9}$
B

$\frac{5}{9}$
C

$\frac{5}{27}$
D

$\frac{25}{81}$

Solution

$9 x^{2} - 18 |x| + 5 = 0$
$x^{2} - 2 |x| + \frac{5}{9} = 0 t h e n t h e t w o e q u a t i o n s a r e$
$x^{2} - 2 x + \frac{5}{9} = 0, x^{2} + 2 x + \frac{5}{9} = 0 i t b e c o m e s (x^{2} - 2 x + \frac{5}{9}) (x^{2} + 2 x + \frac{5}{9}) = 0 p r o d u c t o f r o o t s = \frac{25}{81}$

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