The Quadratic Formula and Complex Solutions

Front

What is the Quadratic Formula?

Back

Front

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

Back

Front

If one solution of a quadratic equation is a + bi, what is the other solution?

Back

The other solution is a - bi, where a is the real part and bi is the imaginary part.

Front

What is the discriminant of a quadratic equation?

Back

Front

How do you determine if a quadratic equation has real or complex solutions by graphing?

Back

By graphing the quadratic equation, if the parabola does not touch or intersect the x-axis, it has complex solutions. If it touches the x-axis, it has real solutions.

Front

Back

Front

What does it mean if a quadratic graph touches the x-axis at one point?

Back

It means the quadratic has one real solution (a repeated root), which occurs when the discriminant is zero.

Front

If a quadratic equation has no real solutions, how many complex solutions does it have?

Back

It has two complex solutions.

Front

What is the significance of the 'i' in complex numbers?

Back

Front

If one solution to a quadratic equation is 3i + 12, what is the other solution?

Back

The other solution is 12 - 3i.