Discriminant

Front

What is the discriminant of a quadratic equation?

Back

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

Front

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

Back

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

Front

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

Back

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

Front

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

Back

A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated or double root.

Front

Given the quadratic equation y = x² + 4x + 4, what is the value of the discriminant?

Back

The discriminant is zero, indicating that there is one repeated real root.

Front

How do you find the value of C in a quadratic equation of the form ax² + bx + c = 0?

Back

C is the constant term in the equation, which can be identified directly from the equation.

Front

If A = -5, B = 1, and C = -5, how do you calculate the discriminant?

Back

Use the formula b² - 4ac: (1)² - 4(-5)(-5) = 1 - 100 = -99.

Front

How do you convert the equation x² - 6 = x into standard form?

Back

Rearrange the equation to x² - x - 6 = 0.

Front

What is the significance of the coefficients A, B, and C in a quadratic equation?

Back

A is the coefficient of x², B is the coefficient of x, and C is the constant term; they determine the shape and position of the parabola.

Front

What is the relationship between the discriminant and the number of solutions to a quadratic equation?

Back

The discriminant determines the nature of the roots: positive for two distinct real roots, zero for one real root, and negative for two complex roots.