Quadratic Equation Part IV
If are the roots of the above equation, then find the value of .
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1 solution
Moderator note:
Great solution.
Is this just a coincidence? Is there any other reason why we might suspect that the answer is 0?
x 3 + 3 x + 9 ⇒ x 3 ⇒ x 9 ⇒ x 9 ⇒ @ 9 £ 9 € 9 ⇒ @ 9 + £ 9 + € 9 = 0 = − 3 ( x + 3 ) = − 3 3 ( x + 3 ) 3 = − 2 7 ( x 3 + 9 x 2 + 2 7 x + 2 7 ) = − 2 7 ( x 3 + 3 x + 9 + 9 x 2 + 2 4 x + 1 8 ) = − 2 7 ( 9 x 2 + 2 4 x + 1 8 ) = − 8 1 ( 3 x 2 + 8 x + 6 ) = − 8 1 ( 3 @ 2 + 8 @ + 6 ) = − 8 1 ( 3 £ 2 + 8 £ + 6 ) = − 8 1 ( 3 € 2 + 8 € + 6 ) = − 8 1 ( 3 ( @ 2 + £ 2 + € 2 ) + 8 ( @ + £ + € ) + 3 ( 6 ) ) = − 8 1 ( 3 [ ( @ + £ + € ) 2 − 2 ( @ £ + £ € + € @ ) ] + 8 ( 0 ) + 1 8 ) = − 8 1 ( 3 [ 0 − 2 ( 3 ) ] + 1 8 ) = − 8 1 ( − 1 8 + 1 8 ) = 0