Question

Find the roots of the quadratic equation given below.
 $ (x + 5)(x - 2) = 0 $

Answer 1

Hint: Root of a quadratic equation is a number which when put in place of $ x $ in the given quadratic equation, gives the value zero as answer. The quadratic equation is given in the form of the product of two linear equations. Use the property that a product is equal to zero if and only if one of the parts of the product is zero.

Complete step-by-step answer:
Any quadratic equation is written in the form
 $ a{x^2} + bx + c = 0 $
One of the methods of solving this quadratic equation is by splitting the middle term. In this method, we split the middle term, $ b $ , of the quadratic equation into two parts such that the product of those two parts is equal to $ ac $ .
After doing that, we take the common term out. Then we further simplify it to convert it into the form,
 $ \Rightarrow (x - \alpha )(x - \beta ) = 0 $
This is called the factor form as $ (x - \alpha ) $ and $ (x - \beta ) $ are the factors of the quadratic equation.
Since, any product equal to zero implies that one of the parts of the product is equal to zero. We write,
 $ \Rightarrow x - \alpha = 0 $ or $ x - \beta = 0 $
Rearranging it we can write
 $ x = \alpha $ or $ x = \beta $
These values $ \alpha $ and $ \beta $ are called the roots of the quadratic equation, $ a{x^2} + bx + c = 0 $
By using the concept explained above, we can write the given quadratic equation as
 $ \Rightarrow (x + 5)(x - 2) = 0 $
It is already simplified to the factor form.
Thus, we can write it further as
 $ x + 5 = 0 $ or $ x - 2 = 0 $
Rearranging it we can write
 $ x = - 5 $ or $ x = 2 $
Thus, the roots of this quadratic equation are $ - 5,2 $
So, the correct answer is “ $ - 5,2 $ ”.

Note: There are other ways of solving a quadratic equation as well. We explained this because this was more comparable to the question. It is not always necessary that every quadratic equation can be solved by the method of splitting the middle term. In such cases we use other methods.