The necessary and sufficient condition for the quadratic function `f(x) = ax^2 + bx + c,` to take both meand negative values is, `b^2 > 4ac,` where `a, b, c e R and a != 0.`

The necessary and sufficient condition for the quadratic function f(x)=ax^(2)+bx+c, to take both meand negative values is,b^(2)>4ac where a,b,ceR and a!=0

Find the condition for which the roots of the quadratic equation ax^2+bx+c=0(ane0) are both negative

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

If in the quadratic function f(x)=ax^(2)+bx+c , a and c are both negative constant, which of the following could be the graph of function f?

(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 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 c(a+b+c) lt 0 lt (a+b+c)a , then

Every quadratic equation ax^(2) + bx + c = 0 ," where "a, b, c in R has

One of the two real roots of the quadratic equation ax^(2)+bx+c=0 is three xx the other Then the value of b^(2)-4ac equals

If a,b,c in R and (a+b+c)c<0 then the quadratic equation p(x)=ax^(2)+bx+c=0 has :