Question

What is a quadratic equation? How can you solve a quadratic equation by factorization method?

Answer 1

Quadratic equation and steps to solve a quadratic equation by factorization method.

Quadratic equation: A quadratic equation in a variable $x$ is an equation of the standard form $a{x}^2+bx+c=0$ , where $a,b,c$are real numbers,$a\ne 0$

Steps to solve a quadratic equation by factorization method are:

• Find two numbers such that their sum is equal to the coefficient of $x$and their product is equal to that product of the coefficient of $x^2$ and the constant value.
• Take the common terms from the available term, to finally obtain the required factors

For example, Factorize the quadratic equation$x^2+2x+1=0$.

• Two numbers such that their sum is equal to the coefficient of that is $2$ and their product is equal to the coefficient of $x^2$ and constant value $1$ their sum is equal to the coefficient of $x$that is $2$ and their product is equal to the product of the coefficient of $x^2$and the constant value$1$. So,$x^2+x+x+1=0$
• Now, taking the common terms from the available term, to finally obtain the required factors as follows:

$$\begin{gathered} x\left(x+1\right)+1\left(x+1\right)=0 \\ \Rightarrow \left(x+1\right)\left(x+1\right)=0 \\ \Rightarrow {\left(x+1\right)}^2=0 \\ \therefore x=-1,-1 \end{gathered}$$

Thus, a quadratic equation is an equation of degree two, and the steps to solve a quadratic equation by factorization method are:

1. Find two numbers such that their sum is equal to the coefficient of $x$ and their product is equal to the product of the coefficient of $x^2$ and the constant value.
2. Take the common terms from the available term, to finally obtain the required factors.