Nature of Roots
Optional Investigation: Investigating the nature of roots
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)
\(x^2 – 6x + 9 = 0\)
\(x^2 – 4x + 3 = 0\)
\(x^2 – 4x – 3 = 0\)
\(x^2 – 4x + 7 = 0\)
- Choose the appropriate words from the table to describe the roots obtained for the equations above.
rational unequal real imaginary not perfect square equal perfect square irrational undefined
- 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?