Question

Find the roots of the equation x2 – 3x – m(m + 3) = 0, where m is a constant​

Answer 1

Answer:

Step-by-step explanation:

Given: equation x  

2

−3x−m(m+3)=0, where m is a constant

To find the roots of the equation

Sol: the given equation is of form ax  

2

+bx+c=0∴a=1,b=−3,c=−m(m+3)

We know the roots of the equation can be find out using the formula,

x=  

2a

−b±  

b  

2

−4ac

​  

 

​  

 

Substituting the values of a, b, c, we get

x=  

2

−(−3)±  

(−3)  

2

−4(1)(−m(m+3)

​  

 

​  

 

⟹x=  

2

3±  

9+4m  

2

+12m

​  

 

​  

 

⟹x=  

2

3±(2m+3)

​  

 

or x=  

2

3+(2m+3)

​  

,x=  

2

3−(2m+3)

​  

 

⟹x=m+3,x=−m are the required roots of the equation.