Any symmetry?

Algebra Level 3

The equation ( x 2 + 3 x + 4 ) 2 + 3 ( x 2 + 3 x + 4 ) + 4 = x { ({ x }^{ 2 }+3x+4) }^{ 2 }+3({ { x }^{ 2 }+3x+4) }+4=x has __________ \text{\_\_\_\_\_\_\_\_\_\_} .

None of its solution real All its solutions real but not all positive Only two of its solution real Two of its solutions positive, two negative

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1 solution

Rajen Kapur
Feb 18, 2016

The concept here is that as plot of f ( x ) = x 2 + 3 x + 4 f(x)=x^2 + 3x + 4 is entirely above y = x y = x there cannot be any solution for f ( f ( x ) ) = x f(f(x))=x .

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