If one root of

7 6 x

2 x 2

x 3 7

=0 is x =-9,Find the other roots

(ans is 2,7)

⇒ [ 7 (7x – 6) – 2 (42 –3x) + x (12 – x2) ] = 0

⇒49x – 42 – 84 + 6x + 12xx3 = 0

⇒67x – 126 – x3 = 0

x3 – 67x + 126 = 0

 

Now since x = – 9 is a root of equation thus

⇒ (x + 9) is a factor of x3 – 67x + 126

 

 

So, x3 – 67x + 126 = 0

⇒(x + 9) (x2 – 9x + 14) = 0

x2 – 9x + 14 = 0

x2 – 7x – 2x + 14 = 0

x (x – 7)2 (x – 7) = 0

⇒(x – 2) (x – 7) = 0

x = 2  or  x = 7

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