Quadratic Formula and the Discriminant

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the Discriminant tell us?

Back

The Discriminant (D = b² - 4ac) indicates the nature of the roots of a quadratic equation. If D > 0, there are 2 real solutions; if D = 0, there is 1 real solution; if D < 0, there are 2 complex (imaginary) solutions.

Front

If the Discriminant is equal to 0, how many solutions are there?

Back

1 Solution.

Front

If the Discriminant is negative, what type of solutions does the quadratic have?

Back

2 Complex (imaginary) Solutions.

Front

What is the value of the Discriminant if there are no real solutions?

Back

A negative number.

Front

Simplify √-45.

Back

3i√5.

Front

What does a positive Discriminant indicate?

Back

It indicates that there are 2 distinct real solutions.

Front

What is the significance of the 'a' coefficient in a quadratic equation?

Back

The 'a' coefficient determines the direction of the parabola: if 'a' > 0, the parabola opens upwards; if 'a' < 0, it opens downwards.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x + a)² = x² + 2ax + a².

Front

How can you determine if a quadratic equation can be factored easily?

Back

If the Discriminant is a perfect square, the quadratic can be factored easily.