MCQ Subject: Quadratic Equations & Inequalities

Which condition ensures the quadratic inequality ax² + bx + c > 0 holds for all real x?

A quadratic equation ax² + bx + c = 0 has no real roots if:

A man’s age is 5 times his son’s age. In 5 years, the man will be 6 times as old as his son. What is the son’s current age?

For a quadratic equation ax² + bx + c = 0, what does the condition b² – 4ac > 0 imply about its roots?

What condition guarantees a quadratic equation ax² + bx + c = 0 has two distinct real roots?

For the quadratic equation x² + 6x + 11 = 0, what can be inferred about its roots?

Solve for y when x > 2 in the inequality 3x – 2y > 6 given x and y are positive integers.

For a quadratic equation ax² + bx + c = 0, where a, b, and c are real numbers, which of the following statements about the nature of its roots is accurate?

For a quadratic equation ax² + bx + c = 0, which condition ensures the equation has exactly two distinct real roots?

If a quadratic equation has roots whose sum is 7 and product is 12, which equation represents this relationship?