Perfect Square Trinomial Calculator

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Choose "Check" to verify whether a trinomial is a perfect square. Choose a "Find" mode to complete a trinomial when one coefficient is missing.
The coefficient of the squared term. Must be a perfect square itself (e.g. 1, 4, 9) for the trinomial to be a perfect square.
The coefficient of the linear (middle) term.
The constant term. Must be a perfect square itself for the trinomial to be a perfect square.
Is a perfect square trinomial?Perfect Square Trinomial
Yes

Yes if the discriminant b² - 4ac equals zero, No otherwise.

Factored form(x + 2)²
Discriminant (b² - 4ac)0
Discriminant (b² - 4ac)0

This is a perfect square trinomial.

  • The discriminant b² - 4ac = 0.0000, which equals zero, confirming a double root.
  • Factored form: (x + 2)²
  • Perfect square trinomials arise naturally when completing the square, a method used in quadratic formula derivation and conic section analysis.

Next stepYou can use this factored form to find roots (set the binomial to zero), or to rewrite the trinomial for completing the square.

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