Know the property

Algebra Level 4

If $f(x) =\displaystyle \prod_{i=1}^{3}(x - a_{i}) + \displaystyle \sum_{i=1}^{3} (a_{i} - x)$

where $a_{i}<a_{i+1}$ then $f(x)=0$ has

only one real root three equal roots three real roots of which 2 are equal 3 distinct real roots

1 solution

Aaaaaa Bbbbbb
Jan 6, 2015

Easy to get answer by trying: $a_{1}=-1, a_{2}=0, a_{3}=1, x \times (x^2-4)=0$ This equation has three roots: -2, 0, 2.