Question

Solve a(2+1)= x(2+1) by using quadratic formula.​

Answer 1

Answer:

x  

2

+x−(a+2)(a+1)=0, Here, a = 1, b = 1, c = -(a + 2)(a + 1)

x=  

2a

−b±  

b  

2

−4ac

​  

 

​  

=  

2(1)

−1±  

1  

2

−4{(a+2)(a+1)}

​  

 

​  

=  

2

−1±  

1−4{−(a  

2

+3a+2)

​  

 

​  

 

x=  

2

−1±  

1+4a  

2

+12a+8

​  

 

​  

=  

2

−1±  

4a  

2

+12a+9

​  

 

​  

=  

2

−1±  

(2a+3)  

2

 

​  

 

​  

=  

2

−1±(2a+3)

​  

 

∴x=  

2

−1+2a+3

​  

 and x=  

2

−1−2a−3

​  

∴x=  

2

2a+2

​  

 and x=  

2

−2a−4

​  

 

x=a+1x=−(a+2)

∴ The roots of x  

2

+x−(a+2)(a+1)=0 are (a+1) and −(a+2)