Solve the quadratic equation using the Quadratic Formula: $$12q^2 + 3q + 8 = 0$$

$$q = \frac{-3 \pm 5i \sqrt{15}}{24}$$ .

What is the discriminant of a quadratic equation?

The discriminant is the expression $$b^2 - 4ac$$ that determines the nature of the roots of the quadratic equation.

What does a positive discriminant indicate?

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

What does a zero discriminant indicate?

A zero discriminant indicates that the quadratic equation has exactly one real solution (a repeated root).

What is an imaginary number?

An imaginary number is a number that can be written as $$bi$$ , where $$b$$ is a real number and $$i$$ is the imaginary unit, defined as $$i = \sqrt{-1}$$ .

How do you express complex solutions?

Complex solutions are expressed in the form $$a + bi$$ , where $$a$$ is the real part and $$b$$ is the imaginary part.

What is the significance of the imaginary unit $$i$$ in solving quadratics?

The imaginary unit $$i$$ allows for the representation of solutions to quadratic equations that do not intersect the x-axis, indicating complex solutions.

What is the general form of a quadratic equation?

The general form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where $$a$$ , $$b$$ , and $$c$$ are constants and @@a eq 0@@.

CW on Section 2.4: Solving quadratics with Complex solutions Flashcard

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What is the Quadratic Formula?

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What does it mean for a quadratic equation to have complex solutions?

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How do you determine if a quadratic equation has complex solutions?

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