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

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_(5)x^(5)+a_(4)x^(4)+a_(3)x^(3)+a_(2)x^(2)+a_(1)x, "where" a_(i),s are real and f (x) = 0 has a positive root alpha_(0). Then f^(prime)(x)=0 has a positive root alpha_1 such that 0 < alpha_1 < alpha_0 f^(prime)(x)=0 has at least two real roots f^('')(x)=0 has at least one real root none of these

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

Let f(x)=ax^(5)+bx^(4)+cx^(3)+dx^(2)+ ex , where a,b,c,d,e in R and f(x)=0 has a positive root. alpha . Then,

Let f(x)=ax^(5)+bx^(4)+cx^(3)+dx^(2)+ ex , where a,b,c,d,e in R and f(x)=0 has a positive root. alpha . Then,

Let F(x)=1+f(x)+(f(x))^2+(f(x))^3 where f(x) is an increasing differentiable function and F(x)=0 has a positive root, then

Let F(x)=1+f(x)+(f(x))^2+(f(x))^3 where f(x) is an increasing differentiable function and F(x)=0 hasa positive root, then

Let F(x)=1+f(x)+(f(x))^(2)+(f(x))^(3) where f(x) is an increasing differentiable function and F(x)=0 hasa positive root then

Let f(x)=ax^3+bx^2+cx+1 has exterma at x=alpha,beta such that alpha beta 0 (c)one positive root if f(alpha) 0 (d) none of these