Multiple choice

The quadratic $x^2+ax+b+1=0$ has roots which are positive integers, then $(a^2+b^2)$ can be equal to

  1. $50$
  2. $37$
  3. $61$
  4. $19$
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A Correct answer
Explanation

Roots are integers p, q. x^2+ax+b+1 = (x-p)(x-q) = x^2 - (p+q)x + pq. So a = -(p+q) and b+1 = pq. Thus a^2+b^2 = (p+q)^2 + (pq-1)^2. If p=1, q=2, a=-3, b=1, a^2+b^2 = 9+1=10. If p=2, q=3, a=-5, b=5, a^2+b^2 = 25+25=50.

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