Unit 2 Flashcard 3 Part A Retake

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 = (-b ± √(b² - 4ac)) / (2a).

To solve a quadratic equation by factoring, express the equation in the form (px + q)(rx + s) = 0, then set each factor to zero and solve for x.

The roots are x = (5 + √3) / 2 and x = (5 - √3) / 2.

To simplify irrational solutions, express them in their simplest radical form, ensuring no perfect squares remain under the square root.

Rearrange the equation to set it to zero: 5x^2 + 13x - 6 = 0.

The solutions are x = 6 and x = -1.

Factoring an equation means rewriting it as a product of its factors, which can then be set to zero to find the solutions.

The roots are x = 0 and x = 9.

Identify a = 1, b = -6, c = -23, then substitute into the formula: x = (6 ± √((-6)² - 4(1)(-23))) / (2(1)).

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, two complex roots.