Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value that determines the nature of the roots of a quadratic equation, calculated as b² - 4ac.

Front

How do you calculate the discriminant for the equation -2x² - x - 1 = 0?

Back

The discriminant is calculated as (-1)² - 4(-2)(-1) = 1 - 8 = -7.

Front

If a function has a discriminant of 4, how many x-intercepts does it have?

Back

It has 2 x-intercepts.

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, only complex roots.

Front

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

Back

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

Front

In the quadratic equation y = ax² + bx + c, what are the coefficients a, b, and c?

Back

a is the coefficient of x², b is the coefficient of x, and c is the constant term.

Front

What is the formula for the discriminant of a quadratic equation?

Back

The formula for the discriminant is D = b² - 4ac.

Front

If the discriminant is b² - 4ac, what does 'b' represent?

Back

In the quadratic equation y = ax² + bx + c, 'b' represents the coefficient of the x term.

Front

What is the leading coefficient in the equation y = x² + 5x + 7?

Back

The leading coefficient is 1 (a = 1).