Question

if x=-9 is a root of | x 3 7, 2 x 2, 7 6 x| =0, then the other two roots are​

Answer 1

Answer:

         The roots are x = - 9, 7, 2

Solution:

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

Expanding along first row, we get

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

or, x³ - 12x - 6x + 42 + 84 - 49x = 0

or, x³ - 67x + 126 = 0

or, x³ + 9x² - 9x² - 81x + 14x + 126 = 0

or, x² (x + 9) - 9x (x + 9) + 14 (x + 9) = 0

[ since x = - 9 is a root, (x + 9) is a factor of the left hand side expression ]

or, (x + 9) (x² - 9x + 14) = 0

or, (x + 9) (x² - 7x - 2x + 14) = 0

or, (x + 9) {x (x - 7) - 2 (x - 7)} = 0

or, (x + 9) (x - 7) (x - 2) = 0

Either x + 9 = 0 or, x - 7 = 0 or, x - 2 = 0

i.e., x = - 9, 7, 2

Therefore, the required solution is

         x = - 9, 7, 2

Answer 2

Hope this answer helps you ^_^ !