Trinomial Solution

Introduction to trinomial solution:

A polynomial with three terms is known as trinomial. One of the three terms is a constant and one of the remaining terms is a constant with a variable and another term is a constant with square of a variable. The constant is an optional. The roots of the trinomial are a solution for the given trinomial. The methods to solve a trinomial are by using quadratic formula or by using factoring method.


General form – Trinomial solution:


The general form of a trinomial is ax ^2+bx+c=0. In this x is a variable and a, b and c are constants.

The value of x is trinomial solution.

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Example problems – Trinomial solution:


Example 1 – Trinomial solution:

Solve the trinomial x ^2+8x+15=0.

Solution:

The given trinomial is x ^2+6x+9=0.

The given trinomial can be written as,

x ^2+3x+3x+9=0.

Take x as common from first two terms

x(x+3)+3x+9=0

Take 3 as common from last two terms

x(x+3)+3(x+3)=0

Take (x+3) as common

(x+3)(x+3)=0

The above product of monomials can be written as

x+3 = 0 and x+3=0

Now solve the above terms for x

So, `x=-3` and `x=-3`

The given trinomial’s solutions are -3 and -3.

So, the answer is -3.

Example 2 – Trinomial solution:

Solve the trinomial x ^2+12x+20=0.

Solution:

The given trinomial is x ^2+12x+20=0.

The given trinomial can be written as,

x ^2+10x+2x+20=0.

Take x as common from first two terms

x(x+10)+2x+20=0

Take 3 as common from last two terms

x(x+10)+2(x+10)=0

Take (x+10) as common

(x+10)(x+2)=0

The above product of monomials can be written as

x+10 = 0 and x+2=0

Now solve the above terms for x

So, `x=-10` and `x=-2`

The given trinomial’s solutions are -10 and -2.

Example 3 – Trinomial solution:

Solve the trinomial 2x ^2+20x+50=0.

Solution:

The given trinomial is 2x ^2+20x+50=0.

The given trinomial can be written as,

2x ^2+10x+10x+50=0.

Take 2x as common from first two terms

2x(x+5)+10x+50=0

Take 10 as common from last two terms

2x(x+5)+10(x+5)=0

Take (x+5) as common

(x+5)(2x+10)=0

The above product of monomials can be written as

x+5 = 0 and 2x+10=0

Now solve the above terms for x

So, `x=-5 ` and `x=-5`

The given trinomial’s solutions are -5 and -5.

So the solution is -5.