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Let a, b be integers such that all the roots of the equation (x^2+a x+20 ) (x^2+17 x+b )=0 are negative integers. What is the smallest possible value of a + b ?

Correct answer

25

Step-by-step solution

aligned & so a>0 and b>0 since sum of roots 0 & ( since 20=(1 20) (2 10) or (4 5) & a=9 & -17= + ( ) (-1,-16),(-2,-15),(-8,-9) & b=16 & (a+b)_ =a_ +b_ =9+16=25 aligned

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