3.1 - 3.4 Extra Review

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

The solutions are $$x = -11$$ and $$x = -4$$ .

The result is $$-12 - 6i$$ .

The result is $$1 - 8i$$ .

The solutions are $$x = -1$$ and $$x = -9$$ .

A complex number is a number that can be expressed in the form $$a + bi$$ , where $$a$$ is the real part and $$b$$ is the imaginary part.

Completing the square is a method used to solve quadratic equations by rewriting them in the form $$(x - p)^2 = q$$ .

The discriminant is the part of the quadratic formula under the square root, given by $$b^2 - 4ac$$ . It determines the nature of the roots.

If the discriminant is positive, there are two real solutions; if it is zero, there is one real solution; if it is negative, there are two complex solutions.

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