Algebra and proofAdditional / Further Maths

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.
  • : no real 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

No real roots

Determine the type of roots using the discriminant.

Identify , and , then substitute into the discriminant .
No real 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
No real 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.
← All Algebra and proof cardsReport a mistake