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CBSE Class 10 Answered

If the roots of x2+bx+c=0 be in the ratio 3:4, show that 12b2=49ac.
Asked by rushabhjain.av | 08 Feb, 2019, 04:01: PM
answered-by-expert Expert Answer
ax2+bx+c=0
roots will be given by
let space straight alpha space and space straight beta space be space the space roots
straight alpha plus straight beta equals fraction numerator negative straight b over denominator straight a end fraction
αβ equals straight c over straight a
straight alpha over straight beta equals 3 over 4
straight alpha equals 3 straight k space and space straight beta equals 4 straight k
12 straight k squared equals straight c over straight a..... left parenthesis 1 right parenthesis
7 straight k equals fraction numerator negative straight b over denominator straight a end fraction rightwards double arrow 49 straight k squared equals straight b squared over straight a squared....... left parenthesis 2 right parenthesis
from space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis
12 straight b squared equals 49 ac
Answered by Arun | 08 Feb, 2019, 05:32: PM

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