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Grade: 12

                        

All the roots of x^3 + a.x^2 + b.x + c are positive integers greater than 2 , and the coefficients satisfy a+b+c+1=2009. Find |a|?

3 years ago

Answers : (1)

Arun
24742 Points
							
Let the roots be r, s, and t. Then they satisfy r + s + t = −a, rs + st + rt = b, and rst = −c. So we
have −(a + b + c + 1) = r + s + t − rs − rt − st + rst − 1 = (r − 1)(s − 1)(t − 1) = 2009 = 7 ∗ 7 ∗ 41.
Thus the roots are 8, 8, and 42, and a = −(r + s + t) = −58.
Hence |a| = 58
3 years ago
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