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Question

# Let a>0,b>0,c>0 then both roots of the equation ax2+bx+c=0

A
are real and negative
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B
have negative real parts
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C
have positive real parts
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D
none of these
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Solution

## The correct option is B have negative real partsSince, a,b,c>0 and ax2+bx+c=0 then,⇒ x=−b2a±√b2−4ac2aCase1: When b2−4ac>0⇒ x=−b2a−√b2−4ac2a and −b2a+√b2−4ac2a both roots are negative.Case2: Ehen b2−4ac=0⇒ x=−b2a i.e., both roots are equal and negative.Case3: When b2−4ac<0⇒ x=−b2a±i√4ac−b22a have negative real part.∴ From above discission both roots have negative real parts.

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