A) a = - b
B) b = - c
C) c = - a
D) b = a + c
Correct Answer: B
Solution :
\[\alpha ,\beta \] be the roots of \[a{{x}^{2}}+bx+c=0\] \[\therefore \alpha +\beta =-b/a\,\,,\,\,\,\,\alpha \beta =c/a\] Now roots are \[\alpha -1,\beta -1\] Their sum, \[\alpha +\beta -2=(-b/a)-2=-8/2=-4\] Their product, \[(\alpha -1)(\beta -1)=\alpha \beta -(\alpha +\beta )+1\] \[=c/a+b/a+1=1\] \[\because \] New equation is \[2{{x}^{2}}+8x+2=0\] \[\therefore b/a=2\] i.e. \[b=2a\], also \[c+b=0\Rightarrow b=-c\].
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