Consider `f(x)=x^2 - |alpha| x - |beta| and g (x) = log_(|alpha|) (x/b)^2-1`.If `f(x) = 0` has roots a and b such that `|a| < |b| and b>1+ |alpha|` then

Consider f (x) = x ^(ln x), and g (x) = e ^(2) x. Let alpha and beta be two values of x satisfying f (x) = g(x)( alpha lt beta) If h (x) = (f (x))/(g (x)) then h'(alpha) equals to:

Consider f (x) = x ^(ln x), and g (x) = e ^(2) x. Let alpha and beta be two values of x satisfying f (x) = g(x)( alpha lt beta) If h (x) = (f (x))/(g (x)) then h'(alpha) equals to:

F(x)=x^(5)+log,(x+sqrt(1+x^(2))) , Then for all alpha, beta in R such that alpha+beta gt 0

F(x)=x^(5)+log,(x+sqrt(1+x^(2))) , Then for all alpha, beta in R such that alpha+beta gt 0

If (x + 2)(x + 3b) = c has roots alpha,beta , then the roots of (x + alpha)(x+beta) + c = 0 are

If (x + 2)(x + 3b) = c has roots alpha,beta , then the roots of (x + alpha)(x+beta) + c = 0 are

If alpha, beta are the roots of (x-a) (x-b)+c=0, c ne 0 , then roots of (alpha beta - c) x^(2) + (alpha + beta) x + 1 = 0 are

If alpha, beta are the roots of a x^(2)+b x+c=0 the equation whose roots are (alpha+beta)^(-1) , alpha^(-1)+ beta^(-1) is

If the roots of a_1x^(2)+b_1x+c_1=0 and alpha_1 , beta_1 and those of a_2x^(2)+b_2x+c_2=0 are alpha_2 , beta_2 such that alpha_1alpha_2=beta_1beta_2=1 then :