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p\( (a f(\mu)0) \) is the necessary and sufficient condition for a particular real number \( \mu \) to lie between the roots of a quadratic equation \( f(x)=0 \), where \( f(x)=a x^{2}+b x+c \). Again if \( f\left(\mu_{1}\right) f\left(\mu_{2}\right)0 \), then exactly one of the roots will lie between \( \mu_{1} \) and \( \mu_{2} \)./ppIf \( a(a+b+c)0(a+b+c) c \), then/pp(1) one root is less than 0 , the other is,greater than 1/pp(2) exactly one of the roots lies in \( (0,1) \)/pp(3) both the roots lie in \( (0,1) \)/pp(4) at least one of the roots lies in \( (0,1) \)/p
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