If `x-r` is a factor of the polynomial `f(x)=a_0x^n+a_1x^(n-1)+.....+a_n` repeated `m` times, `(1ltxlt=n),` then `r` is a root of `f^(prime)(x)=0`repeated `m` times.

If x-c is a factor of order m of the polynomial f(x) of degree n(1

If the remainder of the polynomial a_0 + a_1x + a_2x^2 + .... + a_n x^n when divided by (x - 1) is 1, then which one of the following is correct ?

Let f(x) =a_(0)x^(n)+a_(1)x^(n-1)+...+a_(n)(a_(0)ne0) be a polynomial of degree n . If x+1 is one of its factors, then______.

If f(x) = log ((m(x))/(n(x))), m(1) = n(1) = 1 and m'(1) = n'(1) = 2, " then" f'(1) is equal to

Find the coefficient of x^(n) in the polynomial (x+^(n)C_(0))(x+3^(n)C_(1))xx(x+5^(n)C_(2))...[x+(2n+1)^(n)C_(n)]

If m and n are +ve integers and m>n and if (1+x)^(m+n)(1-x)^(m-n) is expanded as a polynomial in x ,then the coefficient of x^(2) is

If the equation a_0x^n +a_1x^(n-1) +....a_(n-1)x=0 has a positive root alpha prove that the equation na_0x^(n-1) +(n-1)a_1 x^(n-2) + ---+a_(n-1) = 0 also has a positive root smaller than alpha

Evaluate lim_(xrarrc) f(x) where f(x) = a_nx^n+a_(n-1)x^(n-1)+a_(n-2)x^(n-2)+.....+a_2x^2+a_1x^1+a_0