Nature of the Roots 2024

Front

What are the types of roots based on the discriminant?

Back

1. Real and Rational (if discriminant > 0 and a perfect square) 2. Real and Irrational (if discriminant > 0 and not a perfect square) 3. Real and Equal (if discriminant = 0) 4. Imaginary (if discriminant < 0)

Front

What does a discriminant of 0 indicate about the roots of a quadratic equation?

Back

The roots are real and equal.

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

The roots are real and unequal.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

The roots are imaginary.

Front

If the discriminant is equal to 21, what type of roots will the quadratic equation have?

Back

Real, irrational & unequal.

Front

If the discriminant is equal to 49, what type of roots will the quadratic equation have?

Back

Real, rational & unequal.

Front

What is the condition for a parabola to touch the x-axis twice?

Back

The discriminant must be greater than 0 (b² - 4ac > 0).

Front

What is the formula for the discriminant of a quadratic equation ax² + bx + c = 0?

Back

The discriminant is given by D = b² - 4ac.

Front

How can you determine if the roots of a quadratic equation are rational?

Back

The roots are rational if the discriminant is a perfect square.

Front

What is the significance of the vertex of a parabola in relation to its roots?

Back

The vertex indicates the maximum or minimum point of the parabola, which helps in determining the nature of the roots.