Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by the expression b² - 4ac, which determines the nature of the roots of the equation.

Front

In the equation y = ax² + bx + c, what do a, b, and c represent?

Back

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

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 imaginary 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 is the value of the discriminant for the equation y = x² + 4x + 4?

Back

The discriminant is 0, indicating one real solution.

Front

How do you calculate the discriminant for the equation y = 2x² + 3x + 1?

Back

The discriminant is calculated as b² - 4ac = (3)² - 4(2)(1) = 9 - 8 = 1.

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

If the discriminant is equal to 4, how many solutions are there?

Back

There are 2 real solutions.

Front

What type of solutions does a quadratic equation with a discriminant of -3 have?

Back

It has 2 imaginary solutions.

Front

What is the discriminant of the equation y = 3x² - 6x + 2?

Back

The discriminant is (-6)² - 4(3)(2) = 36 - 24 = 12, which is positive.