Let `f(x)=x^3+2x^2+x+5.` Show that `f(x)=0` has only one real root `alpha` such that `[alpha]=-3`

Show that the equation x^(3)+2x^(2)+x+5=0 has only one real root, such that [alpha]=-3 , where [x] denotes the integral point of x

If the equation x^(3)+px^(2)+qx+1=0(p

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

f(x)=a_(5)x^(5)+a_(4)x^(4)+a_(3)x^(3)+a_(2)x^(2)+a_(1)x where a_(i)^( prime)s are real and f(x)=0 has a positive root alpha_(0). Then f'(x)=0 has a positive root alpha_(1) such that 0

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

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

Let f(x)=(e^(x))/(x^(2))x in R-{0}. If f(x)=k has two distinct real roots,then the range of k, is

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

Let g(x)=x^(2)-2x-2 and f(x)=x^(2)+x+alpha . If f(g(x))=0 has no real solution then the set of values of alpha is.