The quadratic `x^2+a x=b+1=0` has roots which are positive integers, then `(a^2+b^2)` can be equal to `50` b. `37` c. `61` d. `19`

Options

A. 50
B. 37
C. 61
D. 19

Answer

1

Explanation

`x^(2) + ax + b + 1 = 0` has positive integral roots `alpha and beta`.
Now, `(alpha + beta) = -a and alphabeta = b + 1`
`rArr (alpha + beta)^(2) + (alphabeta - 1)^(2) = a^(2) + b^(2)`
`rArr a^(2) +b^(2) = (alpha^(2) + 1)(beta^(2) + 1).`
`rArr a^(2) + b^(2)` can be equal to 50 (since other options have prime numbers)