# 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.
 rational unequal real imaginary not perfect square equal perfect square irrational undefined
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?