JEE Advanced Maths: Quadratic Inequalities questions with solutions

Q1. Solve the inequality over the real numbers: (x - 2)(x + 3) >= 0.

1. x <= -3 or x >= 2
2. -3 <= x <= 2
3. x < -3 or x > 2
4. x >= 2 only

Answer: x <= -3 or x >= 2

The product is zero at x = 2 and x = -3. Since the leading coefficient is positive, the expression is non-negative outside the roots (including the roots themselves).