U3T1-T3 Flashcard Review - Extra

The imaginary unit 'i' is defined as $$i = \frac{\text{sqrt}(-1)}{1}$$ . It is used to represent the square root of negative numbers.

$$9i$$ .

$$2i\sqrt{10}$$ .

The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ , used to find the roots of a quadratic equation of the form $$ax^2 + bx + c = 0$$ .

$$b = \pm3$$ .

$$x = \pm2\sqrt{5}$$ .

A real number is any value that can represent a distance along a line, including all rational and irrational numbers.

To simplify square roots of negative numbers, factor out the negative and use the imaginary unit 'i'. For example, $$\sqrt{-a} = i\sqrt{a}$$ .

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction.

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots of the quadratic equation: if positive, two real roots; if zero, one real root; if negative, no real roots.