IKMC 2027 - Grades 11-12 - Self-study SET 2 - Thematic Batch 3 Question 7

Question 7

Consider equation (E): x³−5 x+a=0, where a is real. Which assertion below is certainly true?

1. Equation(E) has at most one integer root for every real a.
2. There exists a real a for which(E) has two integer roots.
3. There exists a real a for which(E) has three integer roots.
4. For every real a, equation(E) has no integer root.
5. For every real a, equation(E) has only irrational roots.