Quadratic Formula with Complex Solutions

Front

What is the Quadratic Formula?

Back

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

Front

What does it mean if a quadratic equation has complex solutions?

Back

Complex solutions occur when the discriminant (b² - 4ac) is negative, resulting in solutions that include imaginary numbers.

Front

Solve x² - 5x + 10 = 0.

Back

(5 - i√15)/2 and (5 + i√15)/2.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac that determines the nature of the roots of the quadratic equation.

Front

If the discriminant is positive, how many real solutions does the quadratic have?

Back

Two distinct real solutions.

Front

If the discriminant is zero, how many real solutions does the quadratic have?

Back

One real solution (a repeated root).

Front

If the discriminant is negative, how many real solutions does the quadratic have?

Back

No real solutions, but two complex solutions.

Front

Solve -2x² + 4x = 9.

Back

(2 - i√14)/2 and (2 + i√14)/2.

Front

How many x-intercepts does a quadratic with 2 real solutions have?

Back

2 x-intercepts.

Front

How many x-intercepts does a quadratic with 1 real solution have?

Back

1 x-intercept.