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Q) If a,b,c are in GP, find the ratio of the roots of the equation ax^2+bx+ c=0.

Asked by Anish 4th September 2018, 4:34 PM
Answered by Expert
Answer:
b2 = ac
begin mathsize 16px style open parentheses straight b over straight a close parentheses squared equals straight c over straight a
open parentheses negative straight b over straight a close parentheses squared equals straight c over straight a
open parentheses straight alpha plus straight beta close parentheses squared equals αβ
straight alpha squared plus straight beta squared plus 2 αβ equals αβ
straight alpha squared plus straight beta squared plus αβ equals 0
open parentheses straight alpha over straight beta close parentheses squared plus straight alpha over straight beta plus 1 equals 0
rightwards double arrow straight alpha over straight beta equals fraction numerator negative 1 plus-or-minus square root of 3 straight i over denominator 2 end fraction space space space space space straight i equals square root of negative 1 end root end style
Answered by Expert 5th September 2018, 12:04 PM
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