The document discusses the discriminant of a quadratic equation ax^2 + bx + c = 0, which is the value b^2 - 4ac. The sign of the discriminant (whether it is zero, positive and a perfect square, positive but not a perfect square, or negative) determines the nature of the roots of the quadratic equation. Examples of quadratic equations with different discriminants are provided.

1. The Nature of the Roots
of a Quadratic Equation

2. The value of the expression
b2 – 4ac is called the
discriminant of the
quadratic equation
ax2 + bx + c = 0.

3. This value can be used to
describe the nature of the
roots of a quadratic equation.
It can be zero, positive and a
perfect square,

4. positive but not perfect
square, or negative.
Example:
1.x2 -4x + 4 = 0 3. x2 + 6x + 3 = 0
2.x2 + 7x + 10 = 0 4. x2 + 2x + 5 = 0