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 ax^2 + bx + c, given by the formula D = b^2 - 4ac. It determines the nature of the roots of the equation.

Front

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

Back

A discriminant of 0 indicates that the quadratic equation has exactly one real root (or a repeated root).

Front

If the discriminant is positive, what can be said about the roots of the quadratic equation?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

What does a negative discriminant signify in terms of the roots of a quadratic equation?

Back

A negative discriminant signifies that the quadratic equation has no real roots, but two complex roots.

Front

Given the quadratic equation 10x^2 - 6 = 0, what is the value of b in the standard form ax^2 + bx + c?

Back

The value of b is 0.

Front

How do you calculate the discriminant for the equation -2x^2 - 6x = 0?

Back

First, identify a = -2, b = -6, and c = 0. Then, use the formula D = b^2 - 4ac: D = (-6)^2 - 4(-2)(0) = 36.

Front

What is the discriminant for the quadratic equation with coefficients a = -5, b = 1, and c = -5?

Back

The discriminant is calculated as D = b^2 - 4ac = (1)^2 - 4(-5)(-5) = 1 - 100 = -99.

Front

How many real solutions does a quadratic equation have if its discriminant is 25?

Back

If the discriminant is 25, the quadratic equation has 2 distinct real solutions.

Front

What is the significance of the discriminant in solving quadratic equations?

Back

The discriminant helps determine the number and type of solutions (real or complex) for a quadratic equation.

Front

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

Back

The formula for the discriminant is D = b^2 - 4ac.