Complex Numbers
Complex Numbers
star_batch_jee_advanced_2025
Grade None
Question:
If all the three roots of $u^3 + bz^2 + cz + d = 0$ have negative real parts, $(a, b, c \in \mathbb{R})$ then
$ab > 0$
$bc > 0$
$ad > 0$
$bc - ad > 0$
Step-by-Step Solution
Key Concept: Each pair of points from different lines intersects at exactly one point.
When selecting 4 points with 2 on one line and 2 on another line, each such selection creates exactly one intersection point. The number of ways to choose 2 points from $m$ points on one line is $\binom{m}{2}$ and 2 points from $n$ points on another line is $\binom{n}{2}$. Therefore, the total number of intersections is $\binom{m}{2} \times \binom{n}{2} = \frac{m(m-1)}{2} \times \frac{n(n-1)}{2} = \frac{m(m-1)n(n-1)}{4}$.
Correct Answer: 1,2,3