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If [alpha]+[beta]+[gamma]=7 then the values of c, where [.] represent the greates integer function are, |
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Answer» (-20,-16) `therefore g(X)=3(x-2)(x-4)` Singn scheme of g(X) for three real roots of f(X)=`x^(3)-9x^(2)+24+c=0` in the INTERVAL (-20,-16) `f(x)=clt0` `f(1)=1-9+24+c=c+16lt0 for forall c in (-20,-1)` `f(2)=8-36+48+c=c+20gt0` `alphain (1,2) or [alpha]=1` `thereforebeta in (3,4)if c in (-18,-16)` now `f(4)=64-144+96+c=16+clt0 if CIN (-18,-16)` or `betan in (3,4) if c in (-18,-16)` Now `f(4)=64-144+96+c=16+clt0 forall c in (-20,16)` or ` gamma(4,5) or [gamma]=4` Thus `[alpha]+[beta]+[gamma]={{:(1+2+4-20ltclt-18),(1+3+4,-18l,tclt-16):}` Now if `c in (-20,-18)` `alphain (1,2) beta (2,3)gamma in (4,5)` or `[alpha]+[beta]+[gamma]=7` If `c in (-18,-16),alpha in (1,2) , beta (3,4) gamma in (4,5) then [alpha+[beta]+[gamma]=8` |
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