Let `f(x)= 3/(x-2)+4/(x-3)+5/(x-4)`. Then `f(x)=0` has (A) exactly one real root in (2,3) (B) exactly one real root in (3,4) (C) at least one real root in (2,3) (D) none of these

If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have (a) no real solution (b) at least one real root in (-1,0) (c) at least one real root in (0,1) (d) none of these

If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have no real solution at least one real root in (-1,0) at least one real root in (0,1) none of these

Prove that the equation 3x^(5)+15x-18=0 has exactly one real root.

Let a in R and f : R rarr R be given by f(x)=x^(5)-5x+a , then (a) f(x)=0 has three real roots if a gt 4 (b) f(x)=0 has only one real root if a gt 4 (c) f(x)=0 has three real roots if a lt -4 (d) f(x)=0 has three real roots if -4 lt a lt 4

If the equation a x^2+2b x-3c=0 has no real roots and ((3c)/4) 0 c=0 (d) None of these

If (x^(2) + 5)/(2) = x - 2 cos (m + n) has at least one real root, the

If p,q,r epsilon R and are distinct the equation (x-p)^5+(x-q)^5+(x-r)^5=0 has (A) four imaginary and one real root (B) two imaginary and three real roots (C) all the roots real (D) none of these

Equation a/(x-1)+b/(x-2)+c/(x-3)=0(a,b,cgt0) has (A) two imaginary roots (B) one real roots in (1,2) and other in (2,3) (C) no real root in [1,4] (D) two real roots in (1,2)

Let a in R and let f: Rvec be given by f(x)=x^5-5x+a , then (a) f(x) has three real roots if a >4 (b) f(x) has only one real roots if a >4 (c) f(x) has three real roots if a<-4 (d) f(x) has three real roots if -4

if f(x)=(x -4) (x-5) (x-6) (x-7) then, (A) f'(x) =0 has four roots (B) three roots f'(x) =0 lie in (4,5) uu(5,6) uu(6,7) (C) the equation f'(x) =0 has only one real root. (D) three roots of f'(x) =0 lie in (3,4) uu (4,5) uu (5,6)