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ISI2020-MMA: 10

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Let $p, q, r \in \mathbb{R}$. If $f(x) = px^{2} + qx + r$ be such that $p + q + r = 3$ and $f (x + y) = f(x) + f(y) + xy$, for all $x, y \in \mathbb{R}$. Then the value of $f(5)$ is.

  1. $25$

  2. $30$

  3. $35$

  4. $40$

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