Quadratic Equations in Mathematics

These flashcards cover key concepts related to quadratic equations, including their forms, properties, and important results.

Quadratic Equation

An equation of the form ax² + bx + c = 0, where a ≠ 0, and a, b, c are coefficients.

Discriminant (D)

The quantity D = b² - 4ac, which helps determine the nature of the roots of the quadratic equation.

Real and Distinct Roots

Occurs when the discriminant D > 0.

Real and Equal Roots

Occurs when the discriminant D = 0.

Complex Roots

Occur when the discriminant D < 0, having non-zero imaginary parts.

Reciprocal Roots

If the roots of ax² + bx + c = 0 are reciprocal, then c = a.

Formation of Quadratic Equation

If the roots are a and ß, the equation is x² - (a + ß)x + aß = 0.

Maximum Value

For a < 0 in ax² + bx + c, the maximum value is calculated at x = -b/(2a).

Minimum Value

For a > 0 in ax² + bx + c, the minimum value is calculated at x = -b/(2a).

Common Roots Condition

For two quadratic equations to have one common root, the condition is (d'c - ac') = (bc' - b'c)(ab' - d).