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Q.

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


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a

-5,2

b

2,3

c

-5,3

d

4,-5 

answer is A.

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Detailed Solution

Any quadratic equation is written in the form
 ax2+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,
 ⇒(x−α)(x−β)=0
This is called the factor form as (x−α) and (x−β) 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,
 ⇒x−α=0 or x−β=0
Rearranging it we can write
 x=α or x=β
These values α and β are called the roots of the quadratic equation, ax2+bx+c=0
By using the concept explained above, we can write the given quadratic equation as
 ⇒(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 ”.
 
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