Question

Find the nature of roots of ax²+bx+c= 0, a>0,b=0,c>0.​

Answer 1

Answer:

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

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