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

For what value of a, does the function f (x) = x ^(5) - 5x + a has three real roots ?

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

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

Let f:R rarr R and f(x)=x^(3)+ax^(2)+bx-8. If f(x)=0 has three real roots &f(x) is a bijective,then (a+b) is equal to

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 f(x)=(x-1)(x-2)(x-3)(x-4) then cut of the three roots of f(x)=0

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

Let f(x)=ax^3+bx^2+x+d has local extrema at x=alpha and beta such that alphabetalt0 and f(alpha).f(beta)gt0 . Then the equation f(x)=0 (A) has 3 distinct real roots (B) has only one real which is positive o a.f(alpha)lt0 (C) has only one real root, which is negative a.f(beta)gt0 (D) has 3 equal roots