Factorise, x^2 + 4x + 1 = 0.

Question:

Factorise,

{eq}x^2 + 4x + 1 = 0 {/eq}

Factorization:

Factorization is a method to get all roots of a particular polynomial.

In this question we have given by quadratic equation.

This question will solve by Completing the whole square method . In this method we subtract and add half of coefficient of x to the equation. And so rearrange in order to form a complete whole square term. And then solve according to get required answer.

Answer and Explanation:

We have,

{eq}x^2 + 4x + 1 = 0 {/eq}

Now,

In order to factorize given quadratic equation we need to use Completing the Whole Square Method

{eq}x^2 + 4x + 1 = 0 \\ x^2 + 4x + 1 + (2)^2 - (2)^2 = 0 \\ x^2 + 4x + (2)^2 + 1 - (2)^2 = 0 \\ (x+2)^2 + 1 - (2)^2 = 0 \\ (x+2)^2 - 3 = 0 \\ {/eq}

On rearranging,

{eq}x+2 = \pm \sqrt 3 \\ x = \pm \sqrt 3 - 2 \\ {/eq}

Hence roots of given equation are;

{eq}\color{blue}{x_1 = \sqrt 3 - 2, \ x_2 = - \sqrt 3 - 2 } {/eq}


Learn more about this topic:

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Partial Fractions: How to Factorize Fractions with Quadratic Denominators

from Math 104: Calculus

Chapter 13 / Lesson 8
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