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CBSE Class 10 Answered

If one root of  equation  px square +qx +r =0 is double the other show that  2q square  =9pr
Asked by piyushpl9527 | 27 Jun, 2018, 04:28: PM
answered-by-expert Expert Answer
begin mathsize 16px style Let space the space roots space of space the space Quadratic space Equation space pq squared space plus space qr space plus space straight r space equals space 0 space be space straight alpha space and space straight beta. We space know space that comma straight alpha space space plus space straight beta space space equals space fraction numerator negative straight b over denominator straight a end fraction space space and space space αβ space equals space straight c over straight a Here space straight a space equals space straight p comma space straight b space equals space straight q space and space straight c space equals space straight r and space straight beta space equals space 2 straight alpha space space space space space space space space space space space space space space space left parenthesis 1 right parenthesis space... left parenthesis space one space root space is space double space of space other right parenthesis straight alpha space space plus space straight beta space space equals space fraction numerator negative straight b over denominator straight a end fraction space equals space fraction numerator negative straight q over denominator straight p end fraction space rightwards double arrow space straight alpha space space plus space space 2 straight alpha space equals space fraction numerator negative straight q over denominator straight p end fraction space....... from space left parenthesis 1 right parenthesis rightwards double arrow straight alpha space equals fraction numerator negative straight q over denominator 3 straight p end fraction space space..... left parenthesis 2 right parenthesis space αβ space equals space straight c over straight a space equals space straight r over straight p rightwards double arrow straight alpha space space cross times space 2 straight alpha space equals space straight r over straight p rightwards double arrow straight alpha squared space equals fraction numerator straight r over denominator 2 straight p end fraction space rightwards double arrow open parentheses fraction numerator negative straight q over denominator 3 straight p end fraction close parentheses squared space equals space fraction numerator straight r over denominator 2 straight p end fraction space space space...... from space left parenthesis 2 right parenthesis rightwards double arrow 2 straight q squared space equals space 9 pr end style
Answered by Yasmeen Khan | 29 Jun, 2018, 09:37: AM

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CBSE 10 - Maths
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