Learning Resources

Focus D: Roots of Polynomial Equations

Step A

Recall the quadratic formula: .

• The two roots should be complex conjugates of each other, which makes sense as you are to take the plus or minus square root of a negative number.
• The numerator in the quadratic formula always has a real part, -b, and a radical part, .
• If b² - 4ac < 0, then a complex number is the result.
• Because the formula also contains "," when b² - 4ac < 0, there will always be two complex roots that are complex conjugates of each other.