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if alpha,and betha are the roots of x2 -3x+a =o , a belongs R and alpha |
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Answer» Letα,βbetherootsofthegivenequationax +bx+c=0 ∴α+β=− a b
....(1) andαβ= a c
.....(2) Now,theequationhavingroots α 1−α
, β 1−β
willbe x 2 −( α 1−α
+ β 1−β
)x+( α 1−α
)( β 1−β
)=0 ⇒x 2 − αβ 2−(α+β)
x+ αβ 1−(α+β)+αβ
=0 Substitutingforα+βandαβfromequations(1)and(2),weget, x 2 − c 2a+b
x+ c a+b+c
=0 ⇒cx 2 −(2a+b)x+(a+b+c)=0 Thisequationisidenticalwithpx 2 +qx+r=0 ∴comparingthelastterms,weget, r=a+b+c |
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