Quadratic Formula with Complex Solutions & Discriminate

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant (D) indicate in a quadratic equation?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: D > 0 means two distinct real solutions, D = 0 means one real solution, and D < 0 means two complex (imaginary) solutions.

Front

What is the value of the discriminant for the equation 11x² - 9x + 3 = 0?

Back

D = (-9)² - 4(11)(3) = 81 - 132 = -51, indicating two imaginary solutions.

Front

If the discriminant is negative, what can be said about the solutions of the quadratic equation?

Back

If the discriminant is negative, the quadratic equation has two complex (imaginary) solutions.

Front

What is the discriminant of the function f(x) = 3x² - 5x + 8?

Back

D = (-5)² - 4(3)(8) = 25 - 96 = -71, indicating two imaginary solutions.

Front

What does it mean if a quadratic graph does not touch the x-axis?

Back

If a quadratic graph does not touch the x-axis, it means there are no real solutions (the solutions are complex).

Front

Calculate the discriminant for the equation x² + 7x + 13.

Back

D = (7)² - 4(1)(13) = 49 - 52 = -3, indicating two non-real (imaginary) solutions.

Front

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

Back

D = (-2)² - 4(6)(-3) = 4 + 72 = 76, indicating two distinct real solutions.

Front

What is the significance of the term 'imaginary solutions'?

Back

Imaginary solutions occur when the discriminant is negative, indicating that the solutions involve the imaginary unit 'i', where i = √(-1).

Front

What is the relationship between the coefficients a, b, and c in a quadratic equation?

Back

In a quadratic equation ax² + bx + c = 0, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.