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ICSE Class 10 Answered

Find the roots of the following quadratic equation using quadratic formula : abx2 + (b2 – ac)x – bc =0
Asked by gpnkumar0 | 29 Jan, 2018, 08:22: PM
answered-by-expert Expert Answer
begin mathsize 16px style Given space quadratic space equation colon space abx squared plus left parenthesis straight b squared minus ac right parenthesis straight x minus bc equals 0 straight x equals fraction numerator negative left parenthesis straight b squared minus ac right parenthesis plus-or-minus square root of open parentheses straight b squared minus ac close parentheses squared minus 4 left parenthesis ab right parenthesis left parenthesis negative bc right parenthesis end root over denominator 2 ab end fraction space space equals fraction numerator negative left parenthesis straight b squared minus ac right parenthesis plus-or-minus square root of open parentheses straight b squared minus ac close parentheses squared plus 4 ab squared straight c end root over denominator 2 ab end fraction space space equals fraction numerator negative left parenthesis straight b squared minus ac right parenthesis plus-or-minus square root of straight b to the power of 4 minus 2 ab squared straight c plus straight a squared straight c squared plus 4 ab squared straight c end root over denominator 2 ab end fraction space space equals fraction numerator negative left parenthesis straight b squared minus ac right parenthesis plus-or-minus square root of straight b to the power of 4 plus 2 ab squared straight c plus straight a squared straight c squared end root over denominator 2 ab end fraction space space equals fraction numerator negative left parenthesis straight b squared minus ac right parenthesis plus-or-minus square root of left parenthesis straight b squared plus ac right parenthesis squared end root over denominator 2 ab end fraction space space equals fraction numerator negative left parenthesis straight b squared minus ac right parenthesis plus-or-minus left parenthesis straight b squared plus ac right parenthesis over denominator 2 ab end fraction straight x equals space space equals fraction numerator negative left parenthesis straight b squared minus ac right parenthesis plus left parenthesis straight b squared plus ac right parenthesis over denominator 2 ab end fraction comma space straight x space equals fraction numerator negative left parenthesis straight b squared minus ac right parenthesis minus left parenthesis straight b squared plus ac right parenthesis over denominator 2 ab end fraction straight x equals space space equals fraction numerator negative straight b squared plus ac plus straight b squared plus ac over denominator 2 ab end fraction comma space straight x space equals fraction numerator negative straight b squared plus ac minus straight b squared minus ac over denominator 2 ab end fraction straight x equals space space equals fraction numerator 2 ac over denominator 2 ab end fraction comma space straight x space equals fraction numerator negative 2 straight b squared over denominator 2 ab end fraction straight x equals space space equals straight c over straight b comma space straight x space equals fraction numerator negative straight b over denominator straight a end fraction end style
Answered by Rashmi Khot | 30 Jan, 2018, 09:10: AM

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