Nature of Roots

Nature of Roots

Optional Investigation: Investigating the nature of roots

  1. Use the quadratic formula to determine the roots of the quadratic equations given below and take special note of:

    • the expression under the square root sign and
    • the type of number for the final answer (rational/irrational/real/imaginary)
    1. \(x^2 – 6x + 9 = 0\)

    2. \(x^2 – 4x + 3 = 0\)

    3. \(x^2 – 4x – 3 = 0\)

    4. \(x^2 – 4x + 7 = 0\)

  2. Choose the appropriate words from the table to describe the roots obtained for the equations above.
    rationalunequalreal
    imaginarynot perfect squareequal
    perfect squareirrationalundefined
  3. The expression under the square root, \(b^2 – 4ac\), is called the discriminant. Can you make a conjecture about the relationship between the discriminant and the roots of quadratic equations?

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