The polynomial equation $x^3-3 a x^2+\left(27 a^2+9\right) x+2016=0$ has
The polynomial equation $x^3-3 a x^2+\left(27 a^2+9\right) x+2016=0$ has
- [KVPY 2016]
- A
exactly one real root for any real $a$
- B
three real roots for any real $a$
- C
three real roots for any $a \geq 0$, and exactly one real root for any $a < 0$
- D
three real roots for any $a \leq 0$, and exactly one real root for any $a > 0$
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- [AIEEE 2003]
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- [KVPY 2010]
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- [IIT 1984]
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Number of rational roots of equation $x^{2016} -x^{2015} + x^{1008} + x^{1003} + 1 = 0,$ is equal to
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