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3 roots of a biquadratic (Posted on 2021-03-14) Difficulty: 3 of 5
Real numbers a and b are chosen so that each of two quadratic trinomials x2+ax+b and x2+bx+a has two distinct real roots and the product of these trinomials has exactly three distinct real roots.

Determine all possible values of the sum of these three roots.

No Solution Yet Submitted by Danish Ahmed Khan    
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re: Solution | Comment 2 of 3 |
(In reply to Solution by Brian Smith)

I am not clear on one point.  Can't the larger root of one equal the larger root of the other?  Can't the smaller root of one equal the smaller root of the other?  Aren't there two other cases besides the case that was analyzed?
  Posted by Steve Herman on 2021-03-14 18:37:00

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