The Discriminant in Quadratic Equation

y = x² − 2x + 1

• a =1
• b = − 2
• c = 1

Using our general formula, the discriminant is
(-2)² − 4•1 •1 = 4 − 4 = 0
Since the discriminant is zero, we should expect 1 real solution which you can see pictured in the graph below.

y = x² − x − 2 and its solution

• a =1
• b = − 1
• c = − 2
• Discriminant: b² − 4(a)(c) = (-1) ² − 4(1)(-2)
  1 − -8 = 1 + 8 = 9
Since the discriminant is positive, there should be 2 real solutions to this equation.

y = x² − 1

• a = 1
• b = 0
• c = −1
• Discriminant: b² − 4(a)(c) = (0) ² − 4(1)(-1)
  − -4 = 4
Since the discriminant is positive, we have two real solutions. The exact solutions are show below.

y = x² + 4x − 5

• a =1
• b = 4
• c = −5
Since the discriminant is positive, there are two real solutions to this quadratic equation.

y = x² + 4x + 5

• a =1
• b = 4
• c = 5
• the discriminant = b² − 4(a)(c) = 4² − 4(1)(5)
  16 − 20 = - 4
Since the discriminant is negative , there are noreal solutions to this quadratic equation. The only solutions are imaginary.

y = x² + 4

• a =1
• b = 0
• c = 4
• the discriminant = b² − 4(a)(c) = 0² − 4(1)(4)
  − 16
Since the discriminant is negative , there are two imaginary solutions to this quadratic equation.

y = x² + 25

• a =1
• b = 0
• c = 25
• the discriminant = b² − 4(a)(c) = 0² − 4(1)(25)
  − 100 = − 100
Since the discriminant is negative , there are two imaginary solutions to this quadratic equation.