Fill in the blanks

If x = -9 is a root of , then other two roots are ___.

If x = -9 is a root of , then other two roots are 2 and 7.

Explanation:

Given x = -9 is a root of .

⇒ x [x² – 12] – 3 [2x – 14] + 7 [12 – 7x] = 0

⇒ x³ – 12x – 6x + 42 + 84 – 49x = 0

⇒ x³ – 67x + 126 =0

Here, 126 × 1 = 9 × 2 × 7

For x = 2,

⇒ 2³ – 67 (2) + 126 = 134 – 134 = 0

∴ x = 2 is one root.

For x = 7,

⇒ 7³ – 67 (7) + 126 = 469 – 469 = 0

∴ x = 7 is also one root.