Question

please solve this
ill mark as....​

Answer 1

Answer:

2 and 7 .

Step-by-step explanation:

Given :

x = - 9 is root of determinant :

Let's open solve determinant first :

$\displaystyle \left|\begin{array}{ccc}x & 3 & 7 \\2 & x & 2 \\7 & 6 & x\end{array}\right| = 0$

= > x ( x² - 12 ) - 3 ( 2 x - 14 ) + 7 ( 12 - 7 x ) = 0

= > x³ - 12 x - 6 x + 42 + 84 - 49 = 0

= > x³ - 67 x + 126 = 0

Since - 9 is root of above expression :

= > ( x + 9 ) = 0 is one of factor.

Now dividing ( x³ - 67 x + 126 ) by ( x + 9 )

x + 9 ) x³ - 67 x + 126 ( x² - 9 x + 14

           x³ + 9 x²

         -     -      

           0    - 9 x² - 67 x

                  - 9 x² - 81 x

                  +     +      

                      0      + 14 x + 126

                              + 14 x + 126

                              -     -      

                                 0        0

Solving for x :  x² - 9 x + 14 :

= > x² - 9 x + 14 = 0

= > x² - 7 x - 2 x + 14 = 0

= > x ( x - 7 ) - 2 ( x - 7 ) = 0

= > ( x - 7 ) ( x - 2 ) = 0

= > x = 7  OR x = 2

Therefore other roots are 2 and 7 .

Hence we get required answer!.