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. It is given by the formula D = b² - 4ac.

Front

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

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

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

Back

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

Front

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

Back

A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated or double root.

Front

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

Back

D = 4² - 4(2)(2) = 16 - 16 = 0.

Front

If the discriminant of a quadratic equation is 36, how many solutions does it have?

Back

The quadratic equation has 2 distinct real solutions.

Front

What is the discriminant of the equation 3x² - 12x + 9 = 0?

Back

D = (-12)² - 4(3)(9) = 144 - 108 = 36.

Front

For the quadratic equation y = x² + 6x + 9, what is the value of the discriminant?

Back

D = 6² - 4(1)(9) = 36 - 36 = 0.

Front

In the quadratic equation ax² + bx + c, what do the letters 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

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

Back

By evaluating the discriminant: if D > 0, two distinct real roots; if D = 0, one real root; if D < 0, two complex roots.