Let `f(x)=a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x ,` where `a_i ' s` are real and `f(x)=0` has a positive root `alpha_0dot` Then (a)`f^(prime)(x)=0` has a positive root `alpha_1` such that `0alpha_1alpha_0`

Let f(x)=a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x , where a_i ' s are real and f(x)=0 has a positive root alpha_0dot Then f^(prime)(x)=0 has a positive root alpha_1 such that 0

If f(x)=|x a a a x a a a x|=0, then f^(prime)(x)=0a n df^(x)=0 has common root f^(x)=0a n df^(prime)(x)=0 has common root sum of roots of f(x)=0 is -3a none of these

IF alpha and beta are the roots of the equation 3x^(2)-4x+1=0 , form the equation whose roots are alpha^(2)/beta and beta^(2)/alpha.

Let f(x)=ax^3+bx^2+cx+1 has exterma at x=alpha,beta such that alpha beta < 0 and f(alpha) f(beta) < 0 f . Then the equation f(x)=0 has three equal real roots one negative root if f(alpha) (a) 0 and f(beta) (b) one positive root if f(alpha) (c) 0 and f(beta) (d) none of these

If alpha and beta are the roots of 2x^2-5x+3=0 form the equation whose roots are alpha+beta and 1/alpha+1/beta

Let f(x ) = ( alpha x^2 )/(x+1),x ne -1 the value of alpha for which f(a) =a , (a ne 0) is

Let f(x)=(alpha x)/(x+1), x ne -1. Then, for what value of alpha " is " f[f(x)]=x ?

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