Polynomial functionsUnit 1

Classifying quadratic roots with the discriminant

Use the sign of the discriminant to count and classify the roots.

  • First write , with . Calculate .
  • : two distinct real roots. : one repeated real root.
  • : two non-real complex conjugate roots.

Example 1

A repeated real root

Use the discriminant to classify the roots.

Identify , and , then substitute into the discriminant .
One repeated real root.

Example 2

A non-real conjugate pair

Determine the type of roots using the discriminant.

Identify , and , then substitute into the discriminant .
Two non-real complex conjugate roots.

Your turn

Question 1

Use the discriminant to classify the roots.

Check answer
Two distinct real roots.
Question 2

Use the discriminant to classify the roots.

Check answer
One repeated real root.
Question 3

Use the discriminant to classify the roots.

Check answer
Two non-real complex conjugate roots.
Question 4

Use the discriminant to classify the roots.

Check answer
Two distinct real roots.
Question 5

Use the discriminant to classify the roots.

Check answer
One repeated real root.
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