Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by the formula b² - 4ac, where a, b, and c are coefficients in the quadratic equation ax² + bx + c = 0.

Front

What does a positive discriminant indicate about the solutions of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a negative discriminant indicate about the solutions of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has two complex (imaginary) solutions.

Front

What does a zero discriminant indicate about the solutions of a quadratic equation?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution (a repeated root).

Front

How do you find the zeros of a quadratic equation in factored form?

Back

Set each factor equal to zero and solve for x. For example, for (x + 10)(x - 2) = 0, the zeros are x = -10 and x = 2.

Front

Calculate the discriminant for the equation 2x² + 4x + 2 = 0.

Back

The discriminant is b² - 4ac = 4² - 4(2)(2) = 16 - 16 = 0.

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.

Front

If the discriminant is 36, how many real solutions does the quadratic equation have?

Back

The quadratic equation has two distinct real solutions.

Front

What is the relationship between the coefficients and the discriminant in a quadratic equation?

Back

The discriminant is calculated using the coefficients of the quadratic equation: D = b² - 4ac.

Front

Solve for the discriminant of the equation x² + 6x + 9 = 0.

Back

The discriminant is b² - 4ac = 6² - 4(1)(9) = 36 - 36 = 0.