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 of a quadratic equation ax² + bx + c = 0.

Front

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

Back

If the discriminant is positive, the quadratic equation has two distinct real solutions.

Front

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

Back

If the discriminant is zero, the quadratic equation has exactly one real solution, also known as a double root.

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.

Front

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

Back

It has 2 x-intercepts.

Front

How many x-intercepts does a quadratic function have if it has one real solution?

Back

It has 1 x-intercept.

Front

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

Back

It has 0 x-intercepts.

Front

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

Back

The zeros are -8i and 8i.

Front

Solve the quadratic equation -2x² + 4x = 9.

Back

The solutions are (2 - i√14)/2 and (2 + i√14)/2.

Front

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

Back

A complex solution is a solution that includes an imaginary number, typically in the form a + bi, where i is the imaginary unit.