Discriminant

Front

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

Back

The discriminant (D) is calculated using the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

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

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

Back

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

Front

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

Back

A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

Front

If the discriminant of a quadratic equation is 25, how many real solutions does it have?

Back

The quadratic equation has 2 real solutions.

Front

How can you determine the nature of the roots of a quadratic equation using the discriminant?

Back

By evaluating the discriminant: if D > 0, there are 2 real solutions; if D = 0, there is 1 real solution; if D < 0, there are 2 complex solutions.

Front

What is the discriminant of the equation 6x² - 2x - 3 = 0?

Back

The discriminant is 76.

Front

Given the quadratic equation 10x² - 6x = 0, what is the value of C in the standard form ax² + bx + c = 0?

Back

The value of C is 0.

Front

What is the significance of the coefficients a, b, and c in the quadratic formula?

Back

The coefficients a, b, and c represent the parameters of the quadratic equation ax² + bx + c = 0, where 'a' determines the parabola's width and direction, 'b' affects the position of the vertex, and 'c' is the y-intercept.

Front

How does the value of 'a' in a quadratic equation affect the graph of the function?

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower for larger absolute values of a).