Quadratic Formula and Discriminant

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant (D) represent in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of a 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

If the discriminant is zero, how many solutions does the quadratic equation have?

Back

If the discriminant is zero, the quadratic equation has exactly one real solution.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real solutions.

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has no real solutions, only complex solutions.

Front

How do you find the discriminant of the quadratic equation 2x² + 4x + 2 = 0?

Back

For the equation 2x² + 4x + 2, a = 2, b = 4, c = 2. The discriminant D = b² - 4ac = 4² - 4(2)(2) = 16 - 16 = 0.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

The first step is to make it equal to 0 by subtracting 3 from both sides: x² + 6x - 16 = 0.

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

What is the completing the square method?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, making it easier to solve for x.

Front

What is the standard form of a quadratic equation?

Back

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