Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c, given by the formula D = b² - 4ac.

Front

If the discriminant is greater than 0, how many solutions does the quadratic equation have?

Back

2 Real solutions.

Front

If the discriminant is less than 0, how many solutions does the quadratic equation have?

Back

2 Imaginary solutions.

Front

What does a discriminant of 0 indicate about the solutions of a quadratic equation?

Back

It indicates that there is 1 real solution (a repeated root).

Front

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

Back

D = 4² - 4(2)(2) = 16 - 16 = 0.

Front

Identify the values of a, b, and c in the quadratic equation: 5x² - 10x + 5 = 0.

Back

a = 5, b = -10, c = 5.

Front

What is the significance of the discriminant in relation to the graph of a quadratic function?

Back

The discriminant determines the number and type of x-intercepts (real solutions) of the graph.

Front

For the quadratic equation x² - 6x + 9 = 0, what is the discriminant?

Back

D = (-6)² - 4(1)(9) = 36 - 36 = 0.

Front

What type of solutions does a quadratic equation with a discriminant of 16 have?

Back

2 Real solutions.

Front

How do you find the discriminant of the equation: 7x² + 3x - 2 = 0?

Back

D = (3)² - 4(7)(-2) = 9 + 56 = 65.