Unit 2 Flashcard 3 Part A Retake

Front

What is the quadratic formula?

Back

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).

Front

How do you solve a quadratic equation by factoring?

Back

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.

Front

What are the roots of the equation 2x^2 - 10x + 11 = 0?

Back

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

Front

How do you simplify irrational solutions?

Back

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

Front

What is the first step in solving the equation 5x^2 + 14x = x + 6 by factoring?

Back

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

Front

What are the solutions to the equation 4x^2 - 24 = 20x?

Back

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

Front

What does it mean to factor an equation?

Back

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

Front

What are the roots of the equation x^2 - 9x = 0?

Back

The roots are x = 0 and x = 9.

Front

How do you apply the quadratic formula to the equation x^2 - 6x - 23 = 0?

Back

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

Front

What is the significance of the discriminant in the quadratic formula?

Back

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.