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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

The discriminant is 0, indicating one real solution.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

There are 2 real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

It has 2 imaginary solutions.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B