Complex number operations and Solving Quadratics

Front

What is the product of the complex numbers (3+8i) and (-2-i)?

Back

The product is 2-19i.

Front

If the discriminant of a quadratic equation is equal to 0, how many real solutions does it have?

Back

It has 1 Real Solution.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

If a function has a discriminant of -3, how many x-intercepts does it have?

Back

It has 0 x-intercepts.

Front

Solve the quadratic equation 5x^2 + 3x - 3 = 0. What are the solutions?

Back

Front

Define 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 does the discriminant of a quadratic equation indicate?

Back

The discriminant indicates the nature of the roots of the quadratic equation: positive for two real solutions, zero for one real solution, and negative for no real solutions.

Front

What is the formula for the quadratic equation?

Back

Front

What is the significance of a negative discriminant?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, only complex solutions.