Perfect Square Trinomial Calculator

The perfect square trinomial calculator is used to solve the quadratic equation step by step.We can know is the quadratic equation have a perfect square or not by the perfect square calculator. Factoring perfect of the second order polynomial in the form of ax2+bx+c=0 for x, where a≠ 0 , we normally use the discriminant to find the factoring perfect square trinomials.

Why we are finding the perfect square?

When we are able to find the nature of the discriminant we are able to find which method can be used to solve the quadratic equation. There are usually the following methods used to solve the quadratic equation.

• The factoring method
• The completing square method
• The quadratic formula method 

What are perfect square trinomials?

Before moving on to how to solve the quadratic equation,it is essential to know What are perfect square trinomials? We already know the trinomial is a polynomial having three terms. A perfect square is a special kind of trinomial, when we multiply two binomials then the resulting term is the perfect square trinomial.

The nature of the discriminant:

The discriminant is a part of the following formula: $$x=\dfrac{-b±\sqrt{{b}^{2}-4ac}}{2a}=\dfrac{-b±\sqrt{\Delta }}{2a}$$

The types  of the discriminant is to define the nature of the quadratic equation. $$\Delta ={b}^{2}-4ac$$

For the equation ax2+bx+c=0, there can be the following possibilities can occur:

1. 1. If Δ<0 then the roots are imaginary(non-real roots) 
   2. If Δ≥0 then the  expression under the square root is non-negative and the roots are real.
   3. If the Δ=0 the roots are equal and we can say there is actually one root of the quadratic equation.
   4. If Δ>0 then the roots would be unequal and then roots are rational. 

Example 1:

Equation : 7x² - 10x + 13 = 0

First we need to find the nature the discriminant Δ = b² - 4ac

a=7,

b= -10,

c= 13

Put the Value in General Form Δ = (-10)2 - 4 x 7 x 13 Δ = 100-364 Δ = -264

Since Δ ≠ 0, your trinomial is not a perfect square. This can be easily calculated by the perfect square trinomial calculator.

Example 2:

Equation : 1x² + 6x + 9 = 0

Let's compute the discriminant Δ = b² - 4ac

a=1,

b= 6,

c= 9

Put the Value in General Form Δ = (6)2 - 4 x 1 x 9 Δ = 36-36 Δ = 0 Since Δ = 0, your trinomial is we have a perfect square! Using the formula p²x² + 2pqx + q² = (px + q)², we obtain 1x² + 6x + 9 = (1x + 3)².  We can check the values by the perfect square calculator.

Example 3:

Equation : 6x² + 5x + 3 = 0

We need to find the type of the discriminant Δ = b² - 4ac

a=6,

b= 5,

c= 3

Put the Value in General Form Δ = (5)2 - 4 x 6 x 3 Δ = 25-72 Δ = -47 Since Δ ≠ 0, your trinomial is not a perfect square. We factorize perfect square trinomials to find whether the discriminant is a perfect square or not. We can find the nature by the perfect square trinomial calculator.

Example 4:

Equation : -5x² - 6x + 5 = 0 The discriminant Δ = b² - 4ac of the following qautatic function is:

a=-5,

b= -6,

c= 5

Put the Value in General Form Δ = (-6)2 - 4 x -5 x 5 Δ = 36--100 Δ = 136 Since Δ ≠ 0, your trinomial is not a perfect square. Factoring perfect square trinomials calculator elaborates the fact the trinomial is a perfect square or not.

Working of the perfect squa re trinomial calculator:

The squaring binomials calculator is easy to use and we can find the perfect square of trinomial by the following procedure:

• Enter the values of the coefficient of quadratic question
• We can only enter the real numbere in the respective fields

Output: The factoring perfect square trinomials showing the nature of the trinomial function:

• The trinomila is a perfect square or not is displayed
• The whole procedure is done for our understanding

FAQs:

What is the procedure to express the trinomial polynomial?

An algebraic equation having three term like ax2 + bx + c = 0 is called the trinomial polynomial. We can find the nature of the trinomial by the square the binomial calculator.

What is the numerical coefficient of the quadratic equation?

The a,b, and c are the numerical coefficient,in the quadratic equation  ax2 + bx + c = 0 . 

What is the leading numerical coefficient?

The number “a” is the leading numerical coefficient. It can never be equal to “0”. 

What is General trinomial?

The general quadratic trinomial is a trinomial of the form ax2 + bx + c, where a, b, and c are real numbers in the equation. We can find the nature and type of the trinomial by the perfect square trinomial calculator.

How you factor a quadratic trinomial:

We make a factor of a quadratic equation that when we add the factors it perfect square factor calculator is equal to the coefficient “b” and when multiple we find the coefficient “c” For example x^2+6x+9=0, can be facrorirized by (x+3)(x+3)=0. We can find the factors by the factoring perfect square trinomials

The final thought:

The perfect square trinomial calculator to find that the trinmial equation is a perfect square or not. The quadratic equations are extensively used to solve various algebraic and financial problems. When we are able to find the solution of the trinomial we are able to predict the result. The Factoring perfect square trinomials is best to find the roots of the trinomial

References:

From the source of Wikipedia: Factorization, Integers, Expressions From the source of schooltutoring: How Is A Binomial Squared, What if the Binomial Has a Minus Sign