Quadratics with Complex Numbers Flashcard

Front

What is the solution to the equation 3k² + 150 = 0?

Back

± 5i

Front

Simplify i^{92}.

Back

1

Front

Solve the equation v^2 + 9 = -19.

Back

{2i√7, -2i√7}

Front

True or false: The solution, root, x-intercept, and zero represent the same thing.

Back

True

Front

Calculate the discriminant of the equation -3x² = 5x + 36.

Back

457

Front

What is the definition of a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a) for the equation ax² + bx + c = 0.

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, two complex roots.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.