5.4 Solving Quadratics by Multiple Methods HW

Front

What are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, completing the square, using the quadratic formula, and graphing.

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation: if D > 0, there are two distinct real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

How do you determine if a quadratic equation has real solutions?

Back

To determine if a quadratic equation has real solutions, calculate the discriminant. If the discriminant is non-negative (D ≥ 0), the equation has real solutions.

Front

What is the significance of a negative discriminant in a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form (x - p)(x - q) = 0, where p and q are the roots, and then set each factor equal to zero.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, allowing for easier solution of the equation.

Front

What is the solution to the equation 6x² - 4 = -5x?

Back

The solutions to the equation 6x² - 4 = -5x are x = {-4/3, 1/2}.

Front

How do you simplify the square root of a negative number, such as √-64?

Back

To simplify the square root of a negative number, express it in terms of imaginary numbers: √-64 = 8i.

Front

What is the solution to the quadratic equation 9u² - 11u + 7 = 0 using the quadratic formula?

Back

The solutions to the equation 9u² - 11u + 7 = 0 using the quadratic formula are u = (11 ± i√131) / 18.