Perfect Square Trinomial Calculator

Perfect Square Trinomial Calculator is a free online tool that displays whether the given trinomial expression is a perfect square trinomial or not. BYJU’S online perfect square trinomial calculator tool makes the calculation faster, and it displays the output in a fraction of seconds.

How to Use the Perfect Square Trinomial Calculator?

The procedure to use the perfect square trinomial calculator is as follows:

Step 1: Enter the input values in the respective fields

Step 2: Now click the button “Factor the Trinomial” to get the output

Step 3: Finally, the result will be displayed in the respective output field

What is Meant by Perfect Square Trinomial?

We know that a trinomial is a polynomial with three terms. A perfect square trinomial is a special type of trinomial. When the binomial terms are multiplied by itself, then the resulting term is called a perfect square trinomial. Let assume that, a function f(x) = ax²+bx+c is said to be a perfect square trinomial if it has double roots. It means that,

If f(a)= 0, f’(a) =0, but f”(a) is not zero, then the trinomial f(x) is said to be a perfect square trinomial. 

Example

Question:

Check whether a given trinomial is a perfect square trinomial: x²-4x+4

Solution:

Given trinomial expression: x²-4x+4

Let f(x)=  x²-4x+4

Now, differentiate the function:

f’(x) = 2x-4

f”(x) = 2

Now, f(2) = f’(2) = 0

But f”(2)= 2

Hence, the given trinomial is a perfect square trinomial.