Let `f(x)=ax^3+bx^2+cx+d=0` have extremum of two different points of opposite signsAssertion (A): Equation `ax^2+bx+c=0` has distinct real roots. , Reason (R): A differentiable function `f(x)` has extremum only at points where `f\'(x)=0`.

The quadratic equation ax^(2)+bx+c=0 has real roots if:

If the equation x^(3)-3ax^(2)+3bx-c=0 has positive and distinct roots, then

If ax^3+bx^2+cx+d has local extremum at two points of opposite signs then roots of equation ax^2+bx+c=0 are necessarily (A) rational (B) real and unequal (C) real and equal (D) imaginary

If the equaion x^(2) + ax+ b = 0 has distinct real roots and x^(2) + a|x| +b = 0 has only one real root, then

If a, b in R and ax^2 + bx +6 = 0,a!= 0 does not have two distinct real roots, then :

Let alpha be the root of the equation ax^2+bx+c=0 and beta be the root of the equation ax^2-bx-c=0 where alphaltbeta Assertion (A): Equation ax^2+2bx+2c=0 has exactly one root between alpha and beta ., Reason(R): A continuous function f(x) vanishes odd number of times between a and b if f(a) and f(b) have opposite signs.

If a,b,c,depsilon R and f(x)=ax^3+bx^2-cx+d has local extrema at two points of opposite signs and abgt0 then roots of equation ax^2+bx+c=0 (A) are necessarily negative (B) have necessarily negative real parts (C) have necessarily positive real parts (D) are necessarily positive

If quadratic equation f(x)=x^(2)+ax+1=0 has two positive distinct roots then

If f(x)=x^3+bx^2+cx+d and 0< b^2 < c , then

If the equation f(x)= ax^2+bx+c=0 has no real root, then (a+b+c)c is (A) =0 (B) gt0 (C) lt0 (D) not real