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.

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.

Front

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

Back

0 x-intercepts.

Front

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

Back

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

Front

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

Back

1 x-intercept.

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.

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.

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.

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.