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 (7*x* – 6) – 2 (42 –3*x*) + *x* (12 – *x*^{2}) ] = 0

⇒49*x* – 42 – 84 + 6*x* + 12*x* – *x*^{3} = 0

⇒67*x* – 126 – *x*^{3} = 0

⇒*x*^{3} – 67*x* + 126 = 0

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

⇒ (*x* + 9) is a factor of *x*^{3} – 67*x* + 126

So, *x*^{3} – 67*x* + 126 = 0

⇒(*x + *9)* *(*x*^{2} – 9*x* + 14) = 0

⇒*x*^{2} – 9*x* + 14 = 0

⇒*x*^{2} – 7*x – *2*x *+ 14 = 0

⇒*x *(*x – *7)* – *2 (*x* – 7) = 0

⇒(*x – *2)* *(*x* – 7) = 0

⇒*x = *2* *or *x* = 7

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