Roots of Quadratics

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by D = b^2 - 4ac. It determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

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

Front

What does a discriminant of zero indicate?

Back

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

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has two complex (non-real) roots.

Front

Calculate the discriminant for the equation 3x^2 - 2x + 1 = 0.

Back

D = (-2)^2 - 4(3)(1) = 4 - 12 = -8 (Complex roots).

Front

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

Back

D = (-4)^2 - 4(1)(4) = 16 - 16 = 0 (One real root).

Front

Calculate the discriminant for the equation 2x^2 + 5x + 3 = 0.

Back

D = (5)^2 - 4(2)(3) = 25 - 24 = 1 (Two distinct real roots).

Front

Calculate the discriminant for the equation 2x^2 - 3x + 1 = 0.

Back

D = (-3)^2 - 4(2)(1) = 9 - 8 = 1 (Two distinct real roots).

Front

What is the formula to find the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: x = (-b ± √D) / (2a), where D is the discriminant.