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Home / Doubts and Solutions/JEE/Mathematics

If a,b,c are positive real numbers, prove that both the roots of ax^2+bx+c=0 have negative real parts.

Asked by Anish 16th August 2018, 4:15 PM
Answered by Expert
Answer:
begin mathsize 18px style straight a comma straight b comma straight c greater than 0 ax squared plus bx plus straight c equals 0 straight x equals fraction numerator negative straight b over denominator 2 straight a end fraction plus-or-minus fraction numerator square root of straight b squared minus 4 ac end root over denominator 2 straight a end fraction three space cases straight b squared minus 4 ac greater than 0 straight x equals fraction numerator negative straight b over denominator 2 straight a end fraction plus fraction numerator square root of straight b squared minus 4 ac end root over denominator 2 straight a end fraction space or space fraction numerator negative straight b over denominator 2 straight a end fraction minus fraction numerator square root of straight b squared minus 4 ac end root over denominator 2 straight a end fraction space space both space real space parts space are space negative straight b squared minus 4 ac equals 0 straight x equals fraction numerator negative straight b over denominator 2 straight a end fraction..... negative space real space part straight b squared minus 4 ac less than 0 straight x equals fraction numerator negative straight b over denominator 2 straight a end fraction plus straight i fraction numerator square root of 4 ac minus straight b squared end root over denominator 2 straight a end fraction space or space fraction numerator negative straight b over denominator 2 straight a end fraction minus straight i fraction numerator square root of 4 ac minus straight b squared end root over denominator 2 straight a end fraction space space both space real space parts space are space negative end style
Answered by Expert 17th August 2018, 11:17 AM
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