Home
Class 12
MATHS
(af(mu) lt 0) is the necessary and suff...

`(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

Promotional Banner

Similar Questions

Explore conceptually related problems

(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

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

f(m)<0.f(x)=ax^(2)-bx+c,m lies between the roots and f(m_(1))f(m_(2))<0 ,then one of the roots will lies between m_(1) and m_(2)

Let f(x) =ax^(2) + bx + c and f(-1) lt 1, f(1) gt -1, f(3) lt -4 and a ne 0 , then

If alpha and beta (alpha lt beta) are the roots of the equation x^(2) + bx + c = 0 , where c lt 0 lt b , then