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TIFR-2016-Maths-A: 9

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Let $p\left (x\right )$ be a polynomial of degree $3$ with real coefficients. Which of the following is possible ?

  1. $p\left ( x \right )$ has no real roots
  2. $p\left ( x \right )$ has exactly $2$ real roots
  3. $p\left ( 1\right )=-1,p\left ( 2 \right )=1, p\left ( 3 \right )=11$ and $p\left ( 4\right )=35$
  4. $i-1$ and $i+1$ are roots of $p\left ( x\right )$, where $i$ is the square root of $-1$

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