N.9 - 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 (roots) of a quadratic equation ax² + bx + c = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant (b² - 4ac) is negative?

Back

If the discriminant is negative, the quadratic equation has two complex (imaginary) solutions and no real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

How many x-intercepts does a quadratic function have if it has two complex solutions?

Back

0 x-intercepts.

Tags

CCSS.HSF-IF.C.7A

Front

What are the solutions to the equation (½)x² + 8 = 0?

Back

The solutions are x = -4i and x = 4i.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Front

If a quadratic has one real solution, how many x-intercepts does it have?

Back

1 x-intercept.

Tags

CCSS.HSF-IF.C.7A

Front

What are the zeros of the function f(x) = x² + 64?

Back

The zeros are -8i and 8i.

Front

What is the significance of the term 'imaginary unit' in complex numbers?

Back

The imaginary unit, denoted as i, is defined as √(-1) and is used to express complex numbers.

Tags

CCSS.HSN.CN.A.1

Front

What is a complex solution in the context of quadratic equations?

Back

A complex solution is a solution that includes an imaginary part, typically expressed in the form a + bi, where a and b are real numbers.

Tags

CCSS.HSN.CN.A.1

Front

What does it mean for a quadratic equation to have a double root?

Back

A double root occurs when the quadratic has one real solution that is counted twice, which happens when the discriminant is zero.

Tags

CCSS.HSA-REI.B.4B

Front

How can you determine the number of real solutions of a quadratic equation?

Back

By evaluating the discriminant (b² - 4ac): if positive, two real solutions; if zero, one real solution; if negative, no real solutions.

Tags

CCSS.HSA-REI.B.4B