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The necessary and sufficient condition f...

The necessary and sufficient condition for which a fixed number `'d'` lies between the roots of quadratic equation `f(x) = ax^2 + bx + c = 0; (a, b, c in R),` is `f(d) < 0.`

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(af(mu) lt 0) is the necessary and sufficient condition for a particular real number mu to lie between the roots of a quadratic equations f(x) =0, where f(x) = ax^(2) + bx + c . Again if f(mu_(1)) f(mu_(2)) lt 0 , then exactly one of the roots will lie between mu_(1) and mu_(2) . If c(a+b+c) lt 0 lt (a+b+c)a , then

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(af(mu) lt 0) is the necessary and sufficient condition for a particular real number mu to lie between the roots of a quadratic equations f(x) =0, where f(x) = ax^(2) + bx + c . Again if f(mu_(1)) f(mu_(2)) lt 0 , then exactly one of the roots will lie between mu_(1) and mu_(2) . If a(a+b+c) lt 0 lt (a+b+c)c , then

(af(mu) lt 0) is the necessary and sufficient condition for a particular real number mu to lie between the roots of a quadratic equations f(x) =0, where f(x) = ax^(2) + bx + c . Again if f(mu_(1)) f(mu_(2)) lt 0 , then exactly one of the roots will lie between mu_(1) and mu_(2) . If |b| gt |a + c| , then

(af(mu) lt 0) is the necessary and sufficient condition for a particular real number mu to lie between the roots of a quadratic equations f(x) =0, where f(x) = ax^(2) + bx + c . Again if f(mu_(1)) f(mu_(2)) lt 0 , then exactly one of the roots will lie between mu_(1) and mu_(2) . If |b| gt |a + c| , then

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