For the quadratic equation x^2 + (8)x + 10 = 0, determine the nature of its roots.

  • one rational and one irrational root
  • no real root
  • two distinct real roots
  • two equal real roots
  • two distinct real roots

For the quadratic equation x^2 + (7)x + 9 = 0, determine the nature of its roots.

  • two equal real roots
  • two distinct real roots
  • no real root
  • one rational and one irrational root
  • two distinct real roots

For the quadratic equation x^2 + (6)x + 8 = 0, determine the nature of its roots.

  • no real root
  • two distinct real roots
  • one rational and one irrational root
  • two equal real roots
  • two distinct real roots

For the quadratic equation x^2 + (5)x + 7 = 0, determine the nature of its roots.

  • one rational and one irrational root
  • no real root
  • two equal real roots
  • two distinct real roots
  • no real root


For the quadratic equation x^2 + (4)x + 6 = 0, determine the nature of its roots.

  • no real root
  • two equal real roots
  • two distinct real roots
  • one rational and one irrational root
  • no real root

For the quadratic equation x^2 + (3)x + 5 = 0, determine the nature of its roots.

  • no real root
  • two equal real roots
  • one rational and one irrational root
  • two distinct real roots
  • no real root