The shortest way of describing the nature of the roots of a quadratic equation is not by solving for the roots but by just using the discriminant of the given quadratic equation.

Below is a specific scenario on how this lesson may help you in some decision making.

A. Apply the idea of the nature of roots of a quadratic equation to visualize, answer if it is possible or not, and then justify your answer.

SCENARIO 1:
Is it possible to make a rectangular park of perimeter 80 m and area 400 m2?

SCENARIO 2:
The sum of the ages of two girls is 20 years. The product of their ages four years ago was 48.Is this possible?

SCENARIO 3:
Is it possible to design a rectangular rice field whose length is twice its width and the area is 800 m2.​