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

The equations x^(2)-2x+1=0,x^(2)-3x+2=0 have a common root then that common root is

If f(x)=2^x-x^2 and f(x)=0 has m solutions f'(x)=0 has n solutions then m+n=

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

Two distinct polynomials f(x) and g(x) defined as defined as follow : f(x) =x^(2) +ax+2,g(x) =x^(2) +2x+a if the equations f(x) =0 and g(x) =0 have a common root then the sum of roots of the equation f(x) +g(x) =0 is -

A polynomial of 6th degree f(x) satisfies f(x)=f(2-x), AA x in R , if f(x)=0 has 4 distinct and 2 equal roots, then sum of the roots of f(x)=0 is

Let f(x)=x^(2)+ax+b, where a,b in R. If f(x)=0 has all its roots imaginary then the roots of f(x)+f'(x)+f(x)=0 are

If f(x) is a polynomial of degree 5 with real coefficientssuch that f(|x|)=0 has 8 real roots,then the number of roots of f(x)=0