Quadratic EquationHard
Question
Let a > 0, b > 0 and c > 0. Then, both the roots of the equation ax2 + bx + c = 0.
Options
A.are real and negative
B.have negative real parts
C.have positive real parts
D.None of the above
Solution
Since, a, b, c > 0
and az2 + bx + c = 0
⇒
Case I When b2 - 4ac > 0
⇒
and 
both roots, are negative.
Case II When b2 - 4ac < 0
⇒
ie, both toots are equal and negative
Case III When b2 - 4ac < 0
⇒
have negative real part.
∴ From sbove discussion both roots have negative real parts.
and az2 + bx + c = 0
⇒
Case I When b2 - 4ac > 0
⇒
and both roots, are negative.Case II When b2 - 4ac < 0
⇒
ie, both toots are equal and negative Case III When b2 - 4ac < 0
⇒
have negative real part. ∴ From sbove discussion both roots have negative real parts.
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