Quadratic Formula with Complex Solutions & Discriminate

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

What does the discriminant tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots of a quadratic equation.

Front

If the discriminant is positive, how many real solutions are there?

Back

2 Real Solutions

Front

If the discriminant is zero, how many real solutions are there?

Back

1 Real Solution

Front

If the discriminant is negative, how many real solutions are there?

Back

No Real Solutions (Complex Solutions exist)

Front

What is the value of the discriminant for the equation 2x² - 4x + 2 = 0?

Back

0 (b² - 4ac = 0) - indicates 1 real solution.

Front

Solve using the quadratic formula: x² - 4x + 4 = 0

Back

x = 2 (double root)

Front

What is the discriminant of the equation 3x² + 6x + 3 = 0?

Back

0 (b² - 4ac = 0) - indicates 1 real solution.

Front

Solve using the quadratic formula: x² + 2x + 5 = 0

Back

x = -1 ± 2i (Complex Solutions)

Front

What is the discriminant of the equation x² + 4x + 8 = 0?

Back

-12 (b² - 4ac < 0) - indicates no real solutions.