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

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

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

Find the value of such that x^(3)-|a|x^(2)+ 3x +4 = 0 has only one real root.

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

The equation (x/(x+1))^2+(x/(x-1))^2=a(a-1) has a. Four real roots if a >2 b.Four real roots if a c. Two real roots if 1 d . No real roots if a<-1

Let f(x)=sinx+a x+bdot Then which of the following is/are true? (a) f(x)=0 has only one real root which is positive if a >1, b 1, b>0. (c) f(x)=0 has only one real root which is negative if a <-1, b < 0. (d) none of these

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero

bb"Statement I" The equation f(x)=4x^(5)+20x-9=0 has only one real root. bb"Statement II" f'(x)=20x^(4)+20=0 has no real root.

Let f(x)=(4-x^(2))^(2//3) , then f has a

Let f(x)=x^2-5x+2 and g(x)=f(x-4). Find the positive root of the equation f(x)=g(2)