Question

Q. In a Quadratic equation ax²+bx+c=0, if a>0, b>0 and c>0 then Both Roots are negative, if a>0 b<0 and c>0 then both Roots are positive, if a>0 , b >0 and c<0 then roots will have opposite signs, What will be the sign of the roots if a>0, b<0 and<0 ?​

Answer 1

Answer:

have negative real parts

Since, a,b,c>0 and ax  

2

+bx+c=0 then,

⇒  x=  

2a

−b

​

±  

2a

b  

2

−4ac

​

 

​

 

Case1: When b  

2

−4ac>0

⇒  x=  

2a

−b

​

−  

2a

b  

2

−4ac

​

 

​

 and  

2a

−b

​

+  

2a

b  

2

−4ac

​

 

​

 both roots are negative.

Case2:  Ehen b  

2

−4ac=0

⇒  x=  

2a

−b

​

 i.e., both roots are equal and negative.

Case3:  When b  

2

−4ac<0

⇒  x=  

2a

−b

​

±i  

2a

4ac−b  

2

 

​

 

​

 have negative real part.

∴  From above discission both roots have negative real parts.

Answer 2

Answer

Both roots have negative real parts.