Polynomial functionsUnit 1

Finding non-real complex zeros

Use the imaginary unit when solving a quadratic with a negative discriminant.

  • Use , so for positive .
  • For real coefficients, non-real roots occur in conjugate pairs.
  • Give all roots, including any real roots from other factors.

Example 1

A quadratic factor

Find all real and non-real complex zeros.

Apply this to both sides.A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.

Example 2

One real root and a conjugate pair

Find all real and non-real complex zeros.

A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.

Your turn

Question 1

Find all solutions.

Check answer
Take both square roots. Use to write the two imaginary roots.
Question 2

Find all solutions.

Check answer
Add the square of half the -coefficient to both sides, then factor the left side as a square.Take both square roots. Use because the number on the right is negative.
Question 3

Find all solutions.

Check answer
Factor the expression.A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.
Question 4

Find all solutions.

Check answer
A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.
Question 5

Find all solutions.

Check answer
A zero product has at least one zero factor. Set each factor equal to zero and solve each equation.
← All Polynomial functions cardsReport a mistake