IKMC 2027 - Grades 11-12 - Self-study SET 9 - Thematic Batch 3 Question 20

Question 20

If $\overline{ABCD}$ is a four-digit number with A≠0, which statement is certainly true about the cubic equation $Ax^3+Bx^2+Cx+D=\overline{ABCD}$?

1. There are three real roots: two negative and one positive.
2. There are three positive real roots.
3. There are three real roots: two positive and one negative.
4. There is exactly one real root, and it is positive.
5. There is exactly one real root, and it is negative.