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. It helps determine the nature of the roots.

Front

If the discriminant is greater than zero, what can be said about the solutions of the quadratic equation?

Back

There are two distinct real solutions.

Front

If the discriminant is equal to zero, what does this indicate about the solutions?

Back

There is exactly one real solution, also known as a repeated or double root.

Front

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

Back

There are no real solutions; the solutions are complex or imaginary.

Front

Calculate the discriminant for the quadratic equation 3x² + 6x + 2 = 0.

Back

D = 6² - 4(3)(2) = 36 - 24 = 12 (positive, so two real solutions).

Front

What is the significance of the discriminant in graphing a quadratic function?

Back

The discriminant helps determine the number of x-intercepts (real solutions) of the graph of the quadratic function.

Front

How does the value of the discriminant affect the vertex of the parabola?

Back

The discriminant does not directly affect the vertex, but it indicates whether the parabola intersects the x-axis at 0, 1, or 2 points.

Front

What is the discriminant of the equation x² - 4x + 4 = 0?

Back

D = (-4)² - 4(1)(4) = 16 - 16 = 0 (indicating one real solution).

Front

For the quadratic equation 2x² + 3x + 5 = 0, what is the discriminant?

Back

D = 3² - 4(2)(5) = 9 - 40 = -31 (negative, indicating no real solutions).

Front

If a quadratic equation has a discriminant of 25, how many solutions does it have?

Back

It has 2 real solutions.