In details

2nd degree equations


What is a 2nd degree equation?

We call the 2nd degree equation in unknown x, every equation of the form:

ax2 + bx + c = 0; The, B, ç GO and

Examples:

  • x2 - 5x + 6 = 0 is a 2nd degree equation with The = 1, B = -5 and ç = 6.

  • 6x2 - x - 1 = 0 is a 2nd degree equation with The = 6, B = -1 and ç = -1.

  • 7x2 - x = 0 is a 2nd degree equation with The = 7, B = -1 and ç = 0.

  • x2 - 36 = 0 is a 2nd degree equation with The = 1, B = 0 and ç = -36.

In equations written in the form ax² + bx + ç = 0 (normal form or reduced form of an equation of the 2nd degree in the unknown x) we call The, B and ç in coefficients.

The is always the coefficient of x²;

B is always the coefficient of x,

ç is the coefficient or independent term.

Complete and incomplete equations

An equation of the 2nd degree is complete When B and ç are nonzero. Examples:

x² - 9x + 20 = 0 and -x² + 10x - 16 = 0 are complete equations.

An equation of the 2nd degree is incomplete When B or ç is equal to zero, or when both are equal to zero. Examples:

  • x² - 36 = 0
    (B = 0)
  • x² - 10x = 0
    (ç = 0)
  • 4x² = 0
    (B = ç = 0)
Next: Roots of a 2nd Degree Equation