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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Front

Solve x² - 5x + 10 = 0.

Back

(5 - i√15)/2 and (5 + i√15)/2.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

Two distinct real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

One real solution (a repeated root).

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

No real solutions, but two complex solutions.

Tags

CCSS.HSA-REI.B.4B

Front

Solve -2x² + 4x = 9.

Back

(2 - i√14)/2 and (2 + i√14)/2.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Front

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

Back

2 x-intercepts.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

1 x-intercept.

Tags

CCSS.HSF-IF.C.7A