Quadratic Equations Module

Practice flashcards based on the Quadratic Equations module, covering key concepts and methods.

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is ax² + bx + c = 0 where a, b, and c are real numbers and a ≠ 0.

What are the methods to solve a quadratic equation?

Quadratic equations can be solved by extracting square roots, factoring, completing the square, and using the quadratic formula.

What does the quadratic formula state?

The quadratic formula states that for the quadratic equation ax² + bx + c = 0, the solutions for x can be found using x = (-b ± √(b² - 4ac)) / 2a.

What is the roots of the quadratic equation x² - 14x + 24 = 0?

The roots are x = 6 and x = 4.

What is a perfect square trinomial?

A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, such as (x + a)² = x² + 2ax + a².

What is the sum and product rule in factoring quadratics?

The sum and product rule states that for the quadratic equation ax² + bx + c = 0, if m and n are the roots, then m + n = -b/a (sum) and mn = c/a (product).

How can you complete the square for the equation x² + 6x = 7?

To complete the square, rewrite as (x + 3)² = 16, therefore x = -3 ± 4, yielding roots of x = 1 and x = -7.

What indicates the number of real roots in a quadratic equation?

The number of real roots is indicated by the discriminant, b² - 4ac; if it is positive, there are two real roots; if zero, one real root; if negative, no real roots.

What are the binomial factors of x² - 24x + 144?

The binomial factors are (x - 12)(x - 12), indicating a double root at x = 12.

If one of the roots of the quadratic equation x² - 5x - 6 = 0 is x1 = 6, what is the other root?

The other root x2 = -1, since the sum of the roots is 5 (6 and -1).